First, I'd highly recommend Zinc Roe's Tickle Tap Toddler Packs 1 & 2, there's lots of simple, but highly interactive stuff in there for kids - and a lot of my daughter's favorites, including things to tap on and explore. She's three now, and still plays with Bug Builder a lot, but her overall favorite at 1-2 years was Sound Shaker.
Roxie's Doors and Adventure might be a little advanced, but are also some of her current favorites. She's been playing a lot with Cyan's The Manhole too, which is probably one of the best kid's exploration games ever... My Play At Home is a great virtual dollhouse, and Baby Apps makes for a great set of faux iPhone activities. Final favorite I'll mention is AWazDat which is a very simple tap on things app. it's got bubbles, too.
EDIT: My daughter can play Little Things, but we have to tell her what to look for.