Hell, I'm not a moderator, but staying on topic keeps everyone happy :-)
As I recall, having a HD with summat like an A500 - I remember getting the A500-HD8+ Impact Series II back in '92 or whenever - means you can run games that run from Workbench from the HD.
As so many Amiga games had their own custom bootblock loaders, more often than not they are not HD installable. However, there are still a fair few that can be installed, such as Sim city for example (IIRC)