I found this amazing website which has a list of online games. It has different set of games for infants and toddlers.
One might wonder about infants ability to play games. Believe me, my daughter was 4 months old when she first started to enjoy these games. That is because all they need to do is tap on keyboard and it displays bright colors, peek-a-boo, animals pop-up along with music.

I don't want my daughter to grow up to be a couch potato playing computer games. So, I limit these activities for 5-10 mins. Let's face it, at this stage, you're mainly looking for something that stops that little baby from crying without frying her brain...or yours. These are the best of the best!
P.S. Don't complain if your keyboard breaks!