The old Dizzy games? And games of that ilk from Codemasters, Mastertronic, etc. Some could be C64 only, so use a C64 emulator :-)
Depending on their age, some simulation games could be fun - SimCity, etc.
I liked platformers - Ghosts and Goblins, Fire and Forget, Rick Dangerous and the like. Also Pinball Dreams and Pinball Fantasies.
For younger people maybe games like Postman Pat and Noddy's Big Adventure.
And don't forget the fun that DPaint can give :-)