While I detest god-mode characters (lowest score: 14) I don't see any specific bonus in playing low-score PCs either. Unless you're a hobbit who inherited a ring from his uncle, most adventurers choose to take up the lifestyle and tend to be the a bit above the common-folk just to survive; if they were clutzy, stupid, weak or frail, they'd be better suited to turnip farming than dungeon raiding.
Of course, that's the nature of D&D; ability score mods mean a lot (esp physical ones) and what is "high" or "low" is dependent on edition (a 13 is good in BD&D, trivial in AD&D, and practically worthless in 4e. Likewise, the value of a 9 is very different in each edition). I think most adventurers (well, the ones who will live to high level) typically have better than average but not godlike stats; something the current point-buys for 3e & 4e kinda-sorta emulate (roughly that range of power).
That said, I see the value in an unlikely hero with a handicap he must overcome; an ox-dumb fighter, a barbarian prone to rash decisions, a socially uncooth ranger, or a frail wizard who can't carry his own gear are all fun characters, but they best serve a extremes to emphasize the "norm" (aka the heroic/better scores of normal adventurers) than as a necessity to "proper role-playing". If ALL fighters have to be dumb, brash, or unpleasant to be around; it gets old quicker than if they had reasonable or heroic scores in the same places.