2-10 :) years. It really depends on what you mean by "dress himself." as dr. Katz pointed out, the main skills needed are there by about 3 years. However, in my experience, the older they get, the more they have their "own ideas" about what to wear, and when to put it on and take it off (their ideas don't always jive with ours!). Expect to be supervising through most of the first decade of life :)
2-3 years. Most children can dress/undress themselves between 2 and 3 years old.