Heck, I’m doing that deliberately, specifically to increase my power. And I have a barbarian without whirlwind, too, and he’s a singer (primary attack is War Cry), at that! On the other hand, I do play online with other Dopers, so they can cover my weak spots.
The only deliberately underpowered thing I’ve ever done in Diablo II was kill the Diablo Clone (hardest monster in the game; only spawns under special circumstances) using a level 55 character and no elite equipment. Once I’d proven that it could be done, though, I leveled up more and gave him some better gear.
Some more of mine:
Minesweeper: Three possibilities. I either don’t mark any mines, or I mark all, and only clear areas using the “clear-all-around-this-square” doubleclick. If I’m feeling particularly masochistic, I crank the number of mines up to 150 (only beaten that twice).
Scorched Earth (old trajectory game): I only ever play against nine computer opponents, all allied against me, all on maximum difficulty, and all in the special triple-turret tank available only to the computer players. I’ve also been known to kill all nine opponents without firing a single offensive weapon (just things like Riot Blast and Dirt Charge), and once I even pulled it off without firing any weapon at all (use a lot of fuel to undermine the enemies and collapse them, or drive on top of them and stomp them to death)
Dark Reign (RTS): I play with one computer ally, against a team of six enemy computers. Then, I try to ensure that my ally kills more units and buildings than I do.
Myth II (Real time tactics): I don’t tolerate any of my units dying at all, and where possible, I go for no damage taken, as well. This actually ends up paying off, since your units accumulate experience if they don’t die, and become more effective in later missions (subtle things like ranged units having better aim, but it makes a difference).
I’ve also done the “no casualties” thing in Starcraft (missions only), and there’s actually one Warcraft III multiplayer map where I can pull it off, too (against seven allied AIs at the “cheating” difficulty level).