It seems that any robust theology of Christian baptism must incorporate and draw from the fact that Jesus himself was baptized, but I rarely hear it mentioned in discussions about baptism. What place does it have in a theology of baptism?
There is an excellent discussion of just this topic among the first parts of St. Nicholas Cabasilas' Our Life in Christ. Any discussion of Epiphany/Theophany also should address specifically this question.
Some thoughts along this line include the following:
In becoming baptized, as the other answers mention, Christ shows us a critical step on the way to salvation, viz. baptism by water and the Holy Spirit. In becoming baptized, Christ's holy body sanctified the water that now baptizes us into his death and resurrection.
Also, in baptism, Christ's divinity was made publicly manifest, by the full Godhead no less, and as a show against the prince of this world that the kingdom of God was now coming in subtle force. To further indicate how fully the kingdom was coming, Christ went out into the wilderness to meet Satan head-on. Now when we become baptized, we too spit on the works of Satan, and now on God's side we too meet Satan to drive him out, not to tolerate his works anymore in these last days.
This by no means exhausts the relationship between our baptism and Christ's. The above references should discuss this at length.
In Matthew 3:15, Jesus stated that he must be baptized to fulfill all righteousness.
Matthew 3:15 (KJV) And Jesus answering said unto him, Suffer it to be so now: for thus it becometh us to fulfil all righteousness. Then he suffered him.
"Christ was circumcised, and observed all the other ordinances of the law of Moses, not with a view to his own justification; but to fulfill the dispensation committed to him by the Lord, the God and Creator of all things." - Wakefield
At the ordination of a new priest the priest must be completely washed. And every year at the Day of Atonement the High Priest was ritually washed in water before fulfilling his duty for the people.
Leviticus 8:6 And Moses brought Aaron and his sons, and washed them with water.
Leviticus 16:4 He shall put on the holy linen coat, and he shall have the linen breeches upon his flesh, and shall be girded with a linen girdle, and with the linen mitre shall he be attired: these are holy garments; therefore shall he wash his flesh in water, and so put them on.
Christ 'fulfilled all righteousness' by being washed (baptized) and anointed (the Holy Ghost came upon Him like a dove) before atoning for the sins of the people.
It becometh us to fulfil all righteousness - It becometh every messenger of God to observe all his righteous ordinances. But the particular meaning of our Lord seems to be, that it becometh us to do (me to receive baptism, and you to administer it) in order to fulfil, that is, that I may fully perform every part of the righteous law of God, and the commission he hath given me. - John Wesley
Christ, who was otherwise perfect (i.e., did not need cleansing from any sin), nevertheless did not exempt Himself from the commandment of baptism. If He was perfect and yet needed baptism "to fulfill all righteousness", how much more do we imperfect souls need it! It is not just for the cleansing of sin and the (re)affirmation of our commitment, it is also to become complete.
Matthew 3:15 (King James Version)
15 And Jesus answering said unto him, Suffer it to be so now: for thus it becometh us to fulfil all righteousness. Then he suffered him.
Right before Jesus was baptised, Jesus said that being baptised was part of "fulfilling all righteousness." We have it from Jesus Himself how important baptism is.