It's too expensive and has dangerous vendor lockin. I myself was burnt 2 years ago and vowed never to return to that platform. Now we use combined Heroku and AWS services. However I do miss GAE though, its deployment is smooth, their auto scaling up is great. It's just that I don't want to be locked in any more.
That being said, we still use GAE as a platform for fast prototypes, as a cron service to keep our Heroku instances up + firing up an EC2 instance every night to run a script for 5 minutes. So we only use GAE when there's minimal risk of being locked in.
OP here. I actually used to use App Engine for Soundslice, about a year before Soundslice launched publicly. It was cool in principle, but it's severely limited to the point where I just couldn't run my app on it. Plus there was wildly varying performance with the database layer.
I'm sure it's gotten better since then (this was circa late 2011), but I'd think long and hard about using App Engine for anything nontrivial.
Compute Engine looks promising. It used to require a subscription to Gold support ($400/month) before you could create any VMs, but they removed this restriction last week.
It still has very limited quotas, though: Maximum of 8 instances or 8 total CPUs. You can request a quota increase through a web form, but I did this a week ago and haven't heard back yet.
Also, it's still in a "limited preview" period, which means your entire zone can go down for weeks for scheduled maintenance, which is pretty inconvenient:
