The Google App Engine (often referred to as GAE) is a really good low cost method to run web apps. Currently the google policy is to allow a generous low usage for free, only charging once usage has exceeded well defined thresholds.
Apps can be developed in several languages, but we favour developing apps in Python due to the availability of excellent documentation. However, it probably would not be hard to use exactly the same argument in favour of Java so really it is matter of personal preference. The Google datastore is a useful storage facility and a range of APIs are available to links to other Google services.
While purists might feel one is getting locked in to a proprietary solution (some thing we here often try to avoid) the level of service and ease of use make the GAE a technically seductive solution for custom applications.
The takeup of tablet PCs and netbooks seems to us to be a great driver for this type of softwarte solution. If you have a specific need for a custom application, then why not drop us a line to see if we can help?