Injini is an AWESOME app. I have the free lite version, and it has enough to keep my Dd busy.
It has puzzles, patterns, memory, pattern, find it, sheep shearing, line tracing, and balloon popping. All of them are made for a toddler's level, and get easier/ harder based on the child's performance. The lite version is limited to the third level of difficulty, which really is perfect for a 2yo. (The full version is $27!!! I would buy it if I had the money, and I rarely buy apps... That's how much I like this app.)
Other than that, Toca games are fun. My DD's favorites are Toca Doctor and Toca Kitchen.
Baby Bus apps are good too. My DD has one for numbers. Which is very easy.