Superheroes, and occasionally high powered Fantasy or Sci-Fi. I have tried Hero time and again with 'normals', and have never liked the way it came out.
Some, I'm sure, will have reasons why it didn't work. Either the players all forgot concept to build 'efficient' characters, making the stats all look the same, or some such.
Nonetheless, I have never liked Hero for games where characteristics are supposed to cover an entirely human range, and I still don't. I have Star Hero and I'll get Fantasy Hero, but I won't likely run either unless it's higher powered.
For 'normal' games, I'll stick with GURPs if I want something I haven't a system for already, or a specific system that fits my desires, such as Traveller, Chivalry & Sorcery, or Rolemaster.
Let it be known, however, that this is simply my opinion. I haven't seen any situation that caused me to change it, but if I saw it work in those genres - SAW it, not merely heard someone claim that it worked for them - then I'd change my mind.