Oddly enough, the worst character concept I've ever seen was one of my own. Not because it was an anime character, not because it was a Mary Sue, but because I deliberately built him with the sole purpose of dying.
During character creation, I initially planned on playing a rogue. However, the rolls I was coming up with for stats were quite abysmal: the first set yielded nothing better than an 11, the second fared worse, but the third set (the DM allowed 3 rerolls) was the best of them all: a 17, two 16s, a 12, a 10, and a 3. Yes, a 3. When the 3 was rolled, the DM got a gigantic shit-eating grin and reminded me that since this was my last reroll I had to stick with these stats. I then decided that I was going to make a "paladin" of Olidammara, the god of rogues and bards. This, of course, meant multiclassing fighter, cleric, and bard, and putting the 3 into Strength. I took Weapon Finesse, got a masterwork rapier, bought the most worthless throwaway magic items possible, filled a Heward's Handy Haversack with useless mundane items, and dumped max skill ranks into Perform.
Combat consisted of putting items together in weird combinations to turn the tides of battle. A lot of plans involved intricate pulley systems and showers of alchemical items. Tried actually attacking straight on, didn't do too well (-4 Strength penalty to damage on a 1d6 rapier didn't work), had to retreat. Scary thing, however, is how long he survived. Went over half the campaign without coming close to death, took the party about that long to figure out what classes I was playing, too.