The Amazon App Store for Android has been doing a Free App of the Day (FAOTD) for over a year I think. Initially there were some good free games and apps, but over time it's been harder to find real good apps/games worth the download on a daily basis. I'd say I probably grab the FAOTD once every 2 weeks, but it's still fun to check every day to see what's free.
It appears Apple may be following suit, realizing people like free stuff, but on a smaller scale. They appear to be offering a free app of the week. The first free app of the week they offered is Cut the Rope Experiments. That is a great choice. Cut the Rope is an excellent game and I can only assume the Experiments sequel is even better, so definitely head out there now and grab it if you have an Apple device.
That is great to see Apple getting on board with some of the things I like about Android, hopefully it is something they continue going forward. That along with the recent Jailbreak has me liking the idea of switching over to the iPhone 5 even more.
Be sure to grab Cut the Rope Experiments while it is still free! And keep an eye on the App Store twitter feed for the latest info. Are you psyched up or what?