I love AppEngine. It takes you time to unwrap your head from SQL and wrap it around the datastore but that's the only thing you have to overcome, believe me.
I'll tell you my story, a desktop developer gone web, starting with php and cheap hosting from godaddy, spending hundreds a month for my pet projects.
Then I learned GAE was free, so why pay for monthly hosting when you can get it for free for your pet projects? I have hundreds of them so I took the plunge and started to learn python. Damn easy, not going back to php, ever.
Don't waste your time with java unless your corporate overlords dictate it. Python is ten times easier and you can go from zero to ninja in one day. Or less.
I started with the hello world example using webapp, no need for frameworks at all, even if you come from django, drop it. Webapp can do it all with a couple of utilities and the template engine (same as django) in a couple of lines.
You'll be amazed at how simple it is to build an app, of any size, once you master the basics about models, sessions, authentication, etc.
You don't need sql connections, chmod configs, apache htaccess, and stuff like that. Just get some data and render it with a template. Fucking easy!
Don't believe me? You lose, not me. Give it a try, you'll be surprised.
I am a happy GAE user and my next startup (which I hope will have a million visits a day) runs on AppEngine and no worries at all about handling them all. Google will be there for me.
GAE 1.4 will come with Channel API, an easy way to send messages back and forth, we just got multitenancy, longer task queues and cron jobs, xmpp, etc.
You get it all at no cost, you pay only a couple of dollars when you need it, when you get slashdotted, dugg or techcrunched. No sweat, no sysadmins running like headless chickens, no server rooms burning.
And that, my friend, that is peace of mind.