We used appengine at a major european car rental company I was working for back then. We deployed a one instance mirror/backup of our booking app which basically cost us nothing. In case our servers, which we kept inhouse, were somehow unreachable we would forward all traffic to appengine and scale up accordingly. After the issue was resolved we would use various mapreduce jobs to migrate new bookings, cancellations etc. back to our servers. The app was written in python with flask on top. To store data we used the NDB Api which was a blast to work with. Overall a really nice experience.
I used it in the past when I learned Python - I built small apps that were just for fun.<p>It's a powerful engine, and has a lot of nice features.<p>I'm pretty happy with starting there, because I moved on to Xcode afterwards.
I used Appengine to host a static website for free, a immigration law firm <a href="http://www.cbulaw.com/" rel="nofollow">http://www.cbulaw.com/</a>. I built it with Django and exported all pages as static files.
I gave it a try, but I found it too annoyingly restricting. I'd rather just roll my own linux servers since I grew up (I know I'm young) with Fedora Core 2.