As fact as character concept goes, quite a lot. Sometimes I come up with a character before I pick power sets. Sometimes after. But they are very much intertwined. Sometimes I skip certain powers if they don't look right. I have a fire melee brute that will not get fire breathing because it wasn't fitting, for instance. Pool powers, including travel powers, are only chosen if they fit the character. Although often several can be made to work and I just pick what's better or my favorite.
If a certain character concept isn't enjoyable to play, it simply gets retired indefinitely and I come up with something else for a dozens of other characters. I am in no rush to be the best level 50 character or even being a level 50 character. Creativity is where it's at!