Funny the past couple of days I've thought about posting a similar post. What I've played with HERO.
Supers (I played a fair amount of Champions until DI came out, very little since)
Fantasy (several D&D Grayhawk based campaigns, plus a number of generic fantasyhero campaigns) this is probably what I've used HERO for the most.
Military
Anti-terrorist
Spy / espionage
lots of Aftermath, Morrow Project and Twilight 2000
A few Call of Cthulhu games
A few pulp games loosely following the Indiana Jones theme
Stalking the night fantastic (modern horror)
A WesternHERO campaign (well ok a few sessions)
A dimension hopping / time travel campaign (I played a 2m tall jet black lizard necromancer named Nerbert who was armed with a Galil ARM and a S&W .44 magnum) unfortunately this game fell apart after a few sessions (the GM flaked out).
A few scifi StarHERO type games (although we didn't have StarHERO since it didn't exist.
A toon game
I've also played in quite a few one shot games of various genres, the heyday of my HERO gaming was in the days of DI, JI and FH3 so its been alongtime for some of the games and I know I'm leaving some out. By the time HERO4 came out we were primarily into FH and Postapacalypse games. Unfortunately I haven't had the chance to break in Fred. 
I have yet to find a genre I was interested in that I couldn't use HERO for. Some games are better for some aspects, particularly detail but I've always been satisfied with HERO.
There were frogs there all right, thousands of them. Their voices beat the night, they boomed and barked and croaked and rattled. They sang to the stars, to the waning moon, to the waving grasses. They bellowed love songs and challenges.
John Steinbeck, Cannery Row
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