You can always look for ideas in the analog gaming world and transform them to a web application.
Board games for instance.
I once wrote a MasterMind. There was even an 'autoplay' option :-)
It was a windows application though (not much web in that time).
Or you could create multiplayer card games...
This is something I have been thinking about of creating myself sometimes... If I only had more time ;-)
I would start with a very basic cardgame 'engine'... basically a table on which x persons can sit and one stack of cards. No rules to start. Cards can be dealt and players can play cards whenever they like.
Then you could implement different cardgames on top of that.
At first only real humans would be able to play with it, but if you get bored again, you could implement "digital players" on top of that.