My son, who is 27 months now, has been using a tablet since about 8 months old. We started mostly with apps that consist of pressing a button to hear animal or machine sounds, he also liked the bubble pop games - especially ones with lots of colors. He caught on really quickly and was able to navigate around my parent's kindle better than them shortly after he turned one. He liked the kneebouncers apps when he was little too, which are just a series of simple cartoon characters that do repetitive things every time you press any button. I also think the book apps on the tablet really helped him to appreciate actual books more, we had problems getting him to listen to a book until we got him some book apps. After watching them with us for awhile he really started liking real books too. The Netflix app is also nice. Lets face it, there's times where having 15 minutes to make dinner, take care of bills, etc are needed and I'm glad my son can watch something to keep him entertained that doesn't have any commercials in it.
I realize that everyone thinks their child is above average, but my son has a great vocabulary, counts to 15 by himself, knows all his colors and shapes, and has an extremely active imagination. I definitely think the time he spends on the iPad helps contribute to that.
Don't listen to the self-righteous assholes telling you your a bad parent because you want to spend time doing something other than peekaboo with you child. Anything that creates a form of bond between you and your child and stimulates their motor and cognitive skills is a valuable tool. It's obvious that a tablet should be just one form of stimulation you provide for your kids, but since there's several hours in the day for play there's plenty of time to include games/tablet use amongst books, puzzles, play-dough, blocks, etc