When I DM, I like to give exceptional knowledge and insight to the players of PCs who have a special niche in which they're experts. For example, the Int 10 Barbarian/Fighter in my last campaign frequently had moments of tactical understanding and insight: even though he was of average intellect, in his field of expertise (he was an army officer), he was very competent and could even tell the mage what to do from time to time. This was a collaboration between the (very intelligent) player and me giving hints.
My own character, whom I play in a different group, is an Int 20, Wis 8, Cha 12 Wizard. I find him a bit hard to roleplay from time to time, but I've already had a lot of fun in pure RP situations, as well. I'm roleplaying his low Wis as mainly affecting his situational awareness and perception: I'm not in Calimshan anymore, but I regularly try and bribe the good, upstanding people of Tethyr, because that's what was socially acceptable back home; people are really depressed and down, so I try and lighten the mood with a bad joke that totally backfires; the situation is dangerous as hell, we have to be vewy, vewy kwiet indeed, but I simply forget about it for a second there and yell at somebody over a minor issue. Stuff like that.
At other times, I try and play against the stereotype for a bit. For example, when I met a childhood friend again after many years (another PC), and she told me about the rough time she's had, I could sympathize well enough and even give insightful advice about how to cope with her personal crisis: I know her, like her, and am focused on her problems when she tells me about them, so my usual 'head-in-the-clouds, not-really-with-you-guys mode' doesn't come into play. My character is rather likable and good with people he comes to care about, after all (Cha 12).
Problem solving, quickly grasping the essentials of a problem, remembering important information, tactical stuff - all those are governed by intelligence, as far as I'm concerned. So in these areas, my character is supposed to be brilliant, and I'm trying to use my brain as efficiently as possible when these things are called for.