Old Testament Messiah Prediction

I suppose that depends on what you count as a "prediction" of Christ's coming. Theologians often consider Genesis 3:15 the first mention of a redeemer. Another early "prediction" that most people recognize is Deuteronomy 18:15. In context, this seems to point to Joshua most clearly, but twice in Acts it is interpreted as a reference to Christ (Acts 3:22; 7:37). Of course, this does not mean that it didn't refer to Joshua, but rather that Joshua was a type of Christ. Daniel 9:25-26 is another popular one.

On the other hand, nowhere does the Old Testament predict specifically that the Christ would be the man Jesus or that he would be God incarnate. Recognition of Jesus Christ as such depended not just on Old Testament typology and expectations (which probably were not well enough understood to demonstrate Jesus as the Christ to most people's satisfaction), but also on the witnesses of the Father and of the Holy Spirit empowering Jesus to work miracles, John the Baptist, etc. (see John 5:31ff.), and Jesus' own testimony about himself. It is worth noting in this regard that Jesus claimed that Scripture testified to his being the Christ. In order to say this, he had to understand prophecy and Scripture to have taught about him typologically rather than directly.

Most of the Bible's predictions regarding Christ aren't really predictions so much as they are offers. God frequently offered to send a redeemer to rescue his people, with the implicit condition that they repent of their sin (compare Jer. 18:1-10 for the basic idea of conditional prophecy). Frequently, the redeemer offered was not Jesus, but rather a more immediate person who was available at the time the prophecy/offer was made. These redeemers were types and foreshadows of Jesus Christ, and helped create in the people an expectation that God would one day send the ulitmate redeemer who would restore the kingdom to Israel and who would reign as the Davidic king forever. Really, in this typological way, the whole Old Testament points to and "predicts" Christ (compare Luke 24:27). Since the whole Old Testament "predicts" Christ in some way, the question then becomes, at what point do we begin to classify a particular passage of Scripture as a "prediction"? How explicit must it be before we think of it in those terms?

We don't have an article specifically on typology on our site, but we do have one on the fundamental conditionality of prophecy: Historical Contingencies and Biblical Predictions by Dr. Richard L. Pratt, Jr.