I use App Engine a ton. I won't try to list all the positives.
Of course "is it flexible enough to run big, serious projects" depends on the requirements of your big serious projects. Feel free to get more specific here, or (better yet) in the google app engine forums.
One thing not mentioned yet that is a legitimate concern applying generally to PaaS offerings including App Engine - that is vendor lock-in. There are some way to address that including choice of apis and frameworks and also projects like AppScale and TyphoonAE.
There is much to evaluate when considering App Engine for your projects. the flexibility of the platform from a technical perspective is one of things.
Also note, watch closely the changes that are coming in pricing and the way that Google is offering the service. You don't want to get caught evaluating the App Engine of 2010 for 2012.
One thing not mentioned yet that is a legitimate concern applying generally to PaaS offerings including App Engine - that is vendor lock-in. There are some way to address that including choice of apis and frameworks and also projects like AppScale and TyphoonAE.
There is much to evaluate when considering App Engine for your projects. the flexibility of the platform from a technical perspective is one of things.
Also note, watch closely the changes that are coming in pricing and the way that Google is offering the service. You don't want to get caught evaluating the App Engine of 2010 for 2012.