I think playing a character with some disabilities can be a lot of fun, but I also do agree people can take it overboard. Unless your playing a completely social game, I don't want to play with a guy whose just a lump character in combat.
Take for example this difference:
1) I'm playing a blind guy. I miss all the time, slow down the party with my crap speed, can't keep a watch, etc.
2) I'm playing a blind guy. But I took blindfight and blindsense 5' (3.0 feat, don't know if its still around). I also worked with the DM to have permanent see invisibility (took a portion of the charcter's starting wealth to "buy" the ability). So I'm good in combat if I can get close, and my party is always aware of invisible creatures. The dm also lets me give everyone a +2 to fear saves around me (if you see a blind guy fighting, how scary could it be?)
Basically its a matter of if you want to play a "weak" character that's fine, but you should try hard to make the character effective to the group, just in a completely different way then they are used to.