Supervillains almost universally require some degree of a goon squad (most of them don't have enough hands to carry all the loot, operate the ridiculous science equipment, point dramatically and speechify), and those goons had to have come from somewhere. Taskmaster runs a goon finishing school, training young, impressionable thugs in the way of polished goondom, arming them with the knowledge necessary to get their asses kicked by Captain America while wearing the same outfit as five thousand other Hydra agents or AIM bucketheads.
That alone makes him a perennial favorite. There's also the fact that his power is fantastic: photographic reflexes, allowing him to imitate anything he sees. He can chuck a shield like Cap, throw those stupid billy clubs around like Daredevil, duel like the Swordsman, juggle like the Death-Throws, hold a giant stick up his ass like Cyclops, go largely forgotten by Marvel editorial for years at a clip like everybody in the New Universe and cook like Iron Chef French. The only reason he loses fights is because he's got a bad habit of pissing off all the Avengers at once, and all the wacky martial arts hijinks in the world ain't trumping Mjolnir.
Plus, his original costume looks like D&D fan art. He somehow looks cool even though his outfit's just a bunch of random crap thrown together. That goes a long way towards making him rule, for some reason.