I have been dipping my toes into the cloud and found some pretty exciting stuff from Amazon. Simple DB is Amazon's web service database and it is now in unlimited beta which means that anyone can sign up and start using the service free (some restrictions), just signup here.
There are loads of technical resources and also a pretty complete FAQ section, which makes getting started really easy. To get up and running check out this page as it gives a pretty easy to follow guide on what you need. There are a bunch of tools available to interact with SimpleDB, one which I have played with is SQLDBExplorer (30 day trial) and a free HTML / Java Script scratchpad tool is available see screen shots below - both need your AWS identifier.
Another interesting development is the public data which is available from AWS, providing a centralized repository of public data sets that can be integrated with AWS cloud-based applications. The current sets include census data and various others, but Amazon are inviting suggestions too for additional sets - check out the UK Stats Authority, Power of Information Task Force and Show Us A Better Way for some ideas on this and general data enrichment.
For some ideas of real examples for Cloud computing check out the recently awarded 2008 AWS Start-Up Challenge and videos of the finalists are here. Oracle have made some interesting announcements too about integration with AWS.