Did John the Baptist baptize Gentiles or only Jews? 

The best "guess" that I have been able to surmise from the Scriptures is that John "probably" did baptize some Gentiles who had converted to Judaism. There are no clear, definitive Bible passages that state he did but there is much Scriptural evidence to indicate that these Gentile proselytes were around at that time which means that more than likely a few would have submitted themselves to John’s baptism.

The Bible shows that there has always been some Gentiles that have joined themselves with the nation of Israel in some capacity. However, even though these individuals lived within the confines of Israel’s borders many were not true religious converts but were actually what the Bible refers to as strangers or proselytes of the gate (Exodus 20:10But the seventh day is the sabbath of the LORD thy God: in it thou shalt not do any work, thou, nor thy son, nor thy daughter, thy manservant, nor thy maidservant, nor thy cattle, nor thy stranger that is within thy gates:
See All...). Even though they were not true proselytes as such, these strangers were expected to honor the Jewish laws and customs.

Leviticus 24:16And he that blasphemeth the name of the LORD, he shall surely be put to death, and all the congregation shall certainly stone him: as well the stranger, as he that is born in the land, when he blasphemeth the name of the Lord, shall be put to death.
See All... And he that blasphemeth the name of the LORD, he shall surely be put to death, and all the congregation shall certainly stone him: as well the stranger, as he that is born in the land, when he blasphemeth the name of the LORD, shall be put to death.

Exodus 20:10But the seventh day is the sabbath of the LORD thy God: in it thou shalt not do any work, thou, nor thy son, nor thy daughter, thy manservant, nor thy maidservant, nor thy cattle, nor thy stranger that is within thy gates:
See All... But the seventh day is the sabbath of the LORD thy God: in it thou shalt not do any work, thou, nor thy son, nor thy daughter, thy manservant, nor thy maidservant, nor thy cattle, nor thy stranger that is within thy gates:

Numbers 15:14-16 [14] And if a stranger sojourn with you, or whosoever be among you in your generations, and will offer an offering made by fire, of a sweet savour unto the LORD; as ye do, so he shall do. [15] One ordinance shall be both for you of the congregation, and also for the stranger that sojourneth with you, an ordinance for ever in your generations: as ye are, so shall the stranger be before the LORD. [16] One law and one manner shall be for you, and for the stranger that sojourneth with you.
See All... And if a stranger sojourn with you, or whosoever be among you in your generations, and will offer an offering made by fire, of a sweet savour unto the LORD; as ye do, so he shall do. One ordinance shall be both for you of the congregation, and also for the stranger that sojourneth with you, an ordinance for ever in your generations: as ye are, so shall the stranger be before the LORD. One law and one manner shall be for you, and for the stranger that sojourneth with you.

In return, these Gentile strangers, whether bond or free were to be accepted and treated fairly by Israel. 

Leviticus 19:33-34 [33] And if a stranger sojourn with thee in your land, ye shall not vex him. [34] But the stranger that dwelleth with you shall be unto you as one born among you, and thou shalt love him as thyself; for ye were strangers in the land of Egypt: I am the LORD your God.
See All... And if a stranger sojourn with thee in your land, ye shall not vex him. But the stranger that dwelleth with you shall be unto you as one born among you, and thou shalt love him as thyself; for ye were strangers in the land of Egypt: I am the LORD your God.

There was however, provision made for those Gentiles that wished to convert to Judaism and become a recognized citizen of Israel. The Lord makes such a distinction between the "stranger that is a sojourner" and an actual religious proselyte who will accept and obey all of the Mosiac covenant:

Exodus 12:48-49 [48] And when a stranger shall sojourn with thee, and will keep the passover to the LORD, let all his males be circumcised, and then let him come near and keep it; and he shall be as one that is born in the land: for no uncircumcised person shall eat thereof. [49] One law shall be to him that is homeborn, and unto the stranger that sojourneth among you.
See All... And when a stranger shall sojourn with thee, and will keep the passover to the LORD, let all his males be circumcised, and then let him come near and keep it; and he shall be as one that is born in the land: for no uncircumcised person shall eat thereof. One law shall be to him that is homeborn, and unto the stranger that sojourneth among you.

Isaiah 56:6Also the sons of the stranger, that join themselves to the LORD, to serve him, and to love the name of the LORD, to be his servants, every one that keepeth the sabbath from polluting it, and taketh hold of my covenant;
See All... Also the sons of the stranger, that join themselves to the LORD, to serve him, and to love the name of the LORD, to be his servants, every one that keepeth the sabbath from polluting it, and taketh hold of my covenant;

Isaiah 56:7Even them will I bring to my holy mountain, and make them joyful in my house of prayer: their burnt offerings and their sacrifices shall be accepted upon mine altar; for mine house shall be called an house of prayer for all people.
See All... Even them will I bring to my holy mountain, and make them joyful in my house of prayer: their burnt offerings and their sacrifices shall be accepted upon mine altar; for mine house shall be called an house of prayer for all people.

We see examples of these Gentile converts throughout the Scriptures such as Ruth the Moabite:

Ruth 1:16And Ruth said, Intreat me not to leave thee, or to return from following after thee: for whither thou goest, I will go; and where thou lodgest, I will lodge: thy people shall be my people, and thy God my God:
See All... And Ruth said, Intreat me not to leave thee, or to return from following after thee: for whither thou goest, I will go; and where thou lodgest, I will lodge: thy people shall be my people, and thy God my God.

Ruth 2:11-12 [11] And Boaz answered and said unto her, It hath fully been shewed me, all that thou hast done unto thy mother in law since the death of thine husband: and how thou hast left thy father and thy mother, and the land of thy nativity, and art come unto a people which thou knewest not heretofore. [12] The LORD recompense thy work, and a full reward be given thee of the LORD God of Israel, under whose wings thou art come to trust.
See All... And Boaz answered and said unto her [Ruth], It hath fully been shewed me, all that thou hast done unto thy mother in law since the death of thine husband: and how thou hast left thy father and thy mother, and the land of thy nativity, and art come unto a people which thou knewest not heretofore. The LORD recompense thy work, and a full reward be given thee of the LORD God of Israel, under whose wings thou art come to trust.

In the book of Esther it is also recorded that there were even Gentile converts during the Jewish captivity:

Esther 8:17And in every province, and in every city, whithersoever the king's commandment and his decree came, the Jews had joy and gladness, a feast and a good day. And many of the people of the land became Jews; for the fear of the Jews fell upon them.
See All... And in every province, and in every city, whithersoever the king's commandment and his decree came, the Jews had joy and gladness, a feast and a good day. And many of the people of the land became Jews; for the fear of the Jews fell upon them.

Other notable Gentiles who rose to prominence in Israel include Doeg the Edomite, Uriah the Hittite, Araunah the Jebusite, Zelek the Ammonite, Ithmah and Ebedmelech the Ethiopians, Rahab the harlot, Naaman the Syrian, etc.

We see these Gentile proselytes are still around in the New Testament as well for we see Jesus rebuking the religious leaders at one point because of their hypocrisy in dealing with these converts. 

Matthew 23:15Woe unto you, scribes and Pharisees, hypocrites! for ye compass sea and land to make one proselyte, and when he is made, ye make him twofold more the child of hell than yourselves.
See All... -Woe unto you, scribes and Pharisees, hypocrites! for ye compass sea and land to make one proselyte, and when he is made, ye make him twofold more the child of hell than yourselves.

They show up at the day of Pentecost with the other Jews also:

Acts 2:8-10 [8] And how hear we every man in our own tongue, wherein we were born? [9] Parthians, and Medes, and Elamites, and the dwellers in Mesopotamia, and in Judaea, and Cappadocia, in Pontus, and Asia, [10] Phrygia, and Pamphylia, in Egypt, and in the parts of Libya about Cyrene, and strangers of Rome, Jews and proselytes,
See All... And how hear we every man in our own tongue, wherein we were born? Parthians, and Medes, and Elamites, and the dwellers in Mesopotamia, and in Judaea, and Cappadocia, in Pontus, and Asia, Phrygia, and Pamphylia, in Egypt, and in the parts of Libya about Cyrene, and strangers of Rome, Jews and proselytes.

Paul also dealt with them on his missionary journey:

Acts 13:42-43 [42] And when the Jews were gone out of the synagogue, the Gentiles besought that these words might be preached to them the next sabbath. [43] Now when the congregation was broken up, many of the Jews and religious proselytes followed Paul and Barnabas: who, speaking to them, persuaded them to continue in the grace of God.
See All... And when the Jews were gone out of the synagogue, the Gentiles besought that these words might be preached to them the next sabbath. Now when the congregation was broken up, many of the Jews and religious proselytes followed Paul and Barnabas: who, speaking to them, persuaded them to continue in the grace of God.

Acts 17:1-4 [1] Now when they had passed through Amphipolis and Apollonia, they came to Thessalonica, where was a synagogue of the Jews: [2] And Paul, as his manner was, went in unto them, and three sabbath days reasoned with them out of the scriptures, [3] Opening and alleging, that Christ must needs have suffered, and risen again from the dead; and that this Jesus, whom I preach unto you, is Christ. [4] And some of them believed, and consorted with Paul and Silas; and of the devout Greeks a great multitude, and of the chief women not a few.
See All... Now when they had passed through Amphipolis and Apollonia, they came to Thessalonica, where was a synagogue of the Jews: And Paul, as his manner was, went in unto them, and three sabbath days reasoned with them out of the scriptures, Opening and alleging, that Christ must needs have suffered, and risen again from the dead; and that this Jesus, whom I preach unto you, is Christ. And some of them believed, and consorted with Paul and Silas; and of the devout Greeks a great multitude, and of the chief women not a few.

A few other notable Gentile proselytes included are the Greeks who were attending the Jewish feast in John 12:20And there were certain Greeks among them that came up to worship at the feast:
See All... and the Ethiopian Eunuch of Acts 8:26-40 [26] And the angel of the Lord spake unto Philip, saying, Arise, and go toward the south unto the way that goeth down from Jerusalem unto Gaza, which is desert. [27] And he arose and went: and, behold, a man of Ethiopia, an eunuch of great authority under Candace queen of the Ethiopians, who had the charge of all her treasure, and had come to Jerusalem for to worship, [28] Was returning, and sitting in his chariot read Esaias the prophet. [29] Then the Spirit said unto Philip, Go near, and join thyself to this chariot. [30] And Philip ran thither to him, and heard him read the prophet Esaias, and said, Understandest thou what thou readest? [31] And he said, How can I, except some man should guide me? And he desired Philip that he would come up and sit with him. [32] The place of the scripture which he read was this, He was led as a sheep to the slaughter; and like a lamb dumb before his shearer, so opened he not his mouth: [33] In his humiliation his judgment was taken away: and who shall declare his generation? for his life is taken from the earth. [34] And the eunuch answered Philip, and said, I pray thee, of whom speaketh the prophet this? of himself, or of some other man? [35] Then Philip opened his mouth, and began at the same scripture, and preached unto him Jesus. [36] And as they went on their way, they came unto a certain water: and the eunuch said, See, here is water; what doth hinder me to be baptized? [37] And Philip said, If thou believest with all thine heart, thou mayest. And he answered and said, I believe that Jesus Christ is the Son of God. [38] And he commanded the chariot to stand still: and they went down both into the water, both Philip and the eunuch; and he baptized him. [39] And when they were come up out of the water, the Spirit of the Lord caught away Philip, that the eunuch saw him no more: and he went on his way rejoicing. [40] But Philip was found at Azotus: and passing through he preached in all the cities, till he came to Caesarea.
See All....

Finally, the most compelling evidence is found in Luke’s account of John baptizing in the Jordan River where we read:

Luke 3:12-14 [12] Then came also publicans to be baptized, and said unto him, Master, what shall we do? [13] And he said unto them, Exact no more than that which is appointed you. [14] And the soldiers likewise demanded of him, saying, And what shall we do? And he said unto them, Do violence to no man, neither accuse any falsely; and be content with your wages.
See All... - Then came also publicans to be baptized, and said unto him, Master, what shall we do? And he said unto them, Exact no more than that which is appointed you. And the soldiers likewise demanded of him, saying, And what shall we do? And he said unto them, Do violence to no man, neither accuse any falsely; and be content with your wages.

Even though the individual accounts of publicans given in the Bible are of Jewish descent, history shows us that there were some Gentile publicans as well at that time which has sparked some debate as to whether all of the publicans mentioned in the above verse were actually Hebrew or not. Which brings us to the soldiers also alluded to. Even if all of the publicans were in deed Jewish the soldiers John addresses in verse 14 are more than likely Gentile (again there has been some speculation as to whether these men are Gentiles or Jewish proselytes who joined affinity with the Roman nation). Though the verse doesn’t say they were baptized explicitly their question is framed exactly like the publicans who we are told were baptized.

As stated previously, there are no verses in the Bible that tell us whether John did or did not baptize any Gentiles but the above Scripture references clearly indicate that there have always been some Gentile converts abiding with the nation of Israel and therefore we can safely assume that some were baptized of him.