My DH has a touchscreen laptop (don't know the brand, but the sort where you can fold the keyboard portion behind so it becomes like a tablet) and uses that to let DS (22 months) navigate Starfall. However, since it's technically DH's work computer, we definitely don't allow any unsupervised use of it; DS sits on his lap to play with it, but he definitely does enjoy getting to navigate on his own.
I'd like to get him started on trying a mouse, though, so I'm going to check out those trackball suggestions a few posts up!