I let my 1.5 yr old son play with my iPad.
I have over 10Gigs of tv shows on it for him and one screen of apps for him. I only bought the 16Gig wifi version.
The iPad was a life saver on our recent vacation. It kept him occupied on the plane. He also enjoys watching a specific 2 minute clip of a Wonder Pets episode just before bed.
But mostly he likes pressing the Home button, flipping through the screens, finding and starting his Dr Seuss book apps, then immediately closing the app, to do it all over again. Strangely, he only likes opening splash screens of apps, not the apps themselves.