I seldom want to forfeit the ability to utilize my own smarts in making decisions for a dumb character, but I do enjoy roleplaying low charisma as
appearing dumb.
My Goliath character from a while back had something like Int 14 Wis 12, but low charisma. I had him speak in common and other languages with irritating grammar errors and slipping in and out of talking about himself in the third person. It worked so well that the other players (not characters) actually got annoyed with it and tried to avoid roleplaying interactions with him whenever possible.

The real great part was in his own thoughts (which would include telepathic speech, but that never happened), or whenever he spoke his native language of Gol-Kaa, his speech was incredibly sophisticated and casually laced with complex vocabulary. But no one spoke Gol-Kaa so to them he was just some nit-wit with a speech impediment.
Currently I'm playing a Dervish who's smart enough for Combat Expertise, and has a positive wisdom as well. She's a tactical genius, but in normal interactions acts very child-like and seemingly unaware of basic knowledge, often engaging in long running questions of "why?", which I try to play up for comedic effect, but for all I know so far it could just be annoying the crap out of the others (I hope not). She acts dumb as a ploy, though, to cause people to underestimate her. She also figures it helps with getting her friends (the party) to dismiss her not-so-good, oftentimes sociopathic ideas/actions as just some other crazy thing out of that crazy head of hers, as opposed to how she'd be viewed if she acted cold and calculating.
I guess what I'm trying to say is, I'm a huge fan of the Obfuscating Stupidity trope. Not so much actual stupidity, though.