GAE is a great tool for new and small projects, that do not require a relational database. I use a range of web hosting solutions.
1) I built www.gaiagps.com on the App Engine, because it was just some brochureware, and a tiny key-value store for the blog part.
2) My colleague also built a web crawler on GAE, because it was just some simple Python scripts that collected web pages. That app actually sends the data over to EC2 though, where more work is done.
3) I host www.trailbehind.com on EC2 because it uses a geo-database (PostGIS) which you would basically have to implement yourself on App Engine.
4) I host TRAC and SVN on WebFaction, because it's off-the-shelf for any slice there.
If I need to do a site in a couple of days, I use GAE. If it's a large or existing project, or has a funky database, I use something else.