We claim my 22-year-old son, a full-time college student, as a dependent. He just got married. Can we continue to claim him as a dependent?

Yes, assuming the other tests for claiming an adult child as a dependent are met. In the case of an adult, non-disabled child, he or she must be under 24, a student for at least 5 months of the year, and not provide more than half of his or her own support (i.e., rent, food, etc). (26 CFR § 1.36B-1(f); 26 CFR § 1.152-1; IRS, Publication 929).