I use ChessBase. For engine autoanalysis, I would use any of the engines that run in the Fritz interface. I prefer to analyze my games myself, and then check my analysis against the engine and PowerBook.
Chess.com saves all the games you play here and will also analyze them. (Click on "Computer Analysis" after the game.) Your premium membership level determines how deep the analysis goes.
Does anybody know a chess program that allows you to save your games in it and analyzes them? Downloading and cost isn't an issue. Thanks!