I want to develop a GAE application using python, but I fear that Google will be the only company able to host the code. Is it possible to run a GAE app on a private server or other host?
(Note that a previous version of the question incorrectly referred to GWT).
You're mixing GWT (a Java to JavaScript compiler) with GAE (the Google server API).
GWT can be served by anybody, after compilation it's just a bunch of .js files; a GAE web app can be served only on Google's servers.
The API is public, and the developer's SDK does work and is OSS; but i don't think it would be a desirable platform for a real service provider. OTOH, according to the Google Code GAE SDK project it's the same infrastructure they use; but it's hard to beleive the backends used to run without GoogleFS, BigTable, MapReduce, etc. could be as scalable as theirs...
Assuming that by GWT you mean GAE (GWT is for Java and anybody can serve it), appscale is probably the best way to host GAE applications anywhere you'd like (including on Amazon EC2 and in your own data center). Anybody can also start a business providing GAE service with AppScale (on Amazon, their own data center, or whatever), which might be attractive for smaller apps (that don't warrant many EC2 or dedicated servers). Anyway, thanks to AppScale and similar efforts, you definitely need not fear "that google will be the only host to host the code".