A charge offered now and then, and used to found other arguments, is that Jesus was illiterate. Let's take a look at what's offered in this regard. Our key source is Meier's Marginal Jew Vol. 1 [269ff].

• Argument #1: 95% of the people in Jesus' time could not read or write, so the odds are that he could not either. While the data is correct (though in Israel the figure may have been more like 90%) it doesn't really provide an argument by itself. It's merely an attempt to stack the deck, and is not based on data concerning the subject, Jesus. By this same argument odds are better that Paul or Matthew could not read or write either.

• Argument #2: Jesus didn't write anything himself, so he must have been illiterate. This is not a very relevant objection, since even literate people hired scribes in the Greco-Roman world. See more here.
• Argument #3: The NT itself shows Jesus was illiterate. Now we get to the primary data. Let's look at the relevant cites:

  John 7:15 And the Jews marvelled, saying, How knoweth this man letters, having never learned?

  "Letters" is gramma and refers to any writings -- letters, notes, scriptures, or even bills of sale (Luke 16:6, And he said, An hundred measures of oil. And he said unto him, Take thy bill, and sit down quickly, and write fifty.) In John it is used to refer to the writings of Moses (5:47), or Scriptures. Here the matter is actually that Jesus never had formal training in the Scriptures: The context of the response is to Jesus' ability to expound the Scriptures, not his ability to read them. Furthermore, it points to Jesus being thought of as literate, since it is clear that they are granting that Jesus "knoweth" his letters -- and are asking "how'd he do that"???

  Luke 4:17-20 And there was delivered unto him the book of the prophet Esaias. And when he had opened the book, he found the place where it was written, The Spirit of the Lord is upon me, because he hath anointed me to preach the gospel to the poor; he hath sent me to heal the brokenhearted, to preach deliverance to the captives, and recovering of sight to the blind, to set at liberty them that are bruised, To preach the acceptable year of the Lord. And he closed the book, and he gave it again to the minister, and sat down. And the eyes of all them that were in the synagogue were fastened on him.

  John 8:8 And again he stooped down, and wrote on the ground.

  The word "wrote" is used to describe typical writing (John 8:17 It is also written in your law, that the testimony of two men is true.) -- admittedly it can mean "engraving" but this is not the majority usage. However, Meier rightly notes that it would even so say nothing about Jesus' level of literacy without any description of the content.

  The Lucan cite Meier says provides "unquestionable proof" of Jesus' literacy -- though he adds that many could dispute this story as a Lucan redaction, a matter beyond our scope here, but which we would point to as being reliant on arbitrary argumentation.

  I'll add one more set of citations from Evans' Fabricating Jesus [38]: There are places where Jesus addresses the Pharisees with the riposte, "Have you not read..?" [Mark 2:25, 12:10, etc.] In an honor-based setting, this sort of challenge is completely unthinkable unless Jesus himself could read, for he would leave himself wide open to the simple counter-riposte (which would seriously shame him) that he could not read himself.

Meier finally decides that the odds, though, are much greater that Jesus was literate even without these cites. He points to Jesus' obviously familiarity with both the OT and the intertestamental writings, to the general attitude in Judaism that "to be able to read and explain the Scriptures was a revered goal for religiously minded Jews," and Jesus' obvious skill at using the Scriptures, and concludes that it is far more likely that Jesus would have to have been literate to have had such skill. He adds that all that would be required for Jesus to have this path open was a pious father (Joseph would fill the bill) and a local synagogue (which Nazareth probably had) to do the teaching. We therefore conclude that the burden of proof would be on those who claim that Jesus was not literate.