With that in mind, the best thing for most companies to do is to first experiment with some of the simple cloud services that are available. The great thing about these services is that they are already widely used. If something goes wrong with them, it won't be just your site that's in peril. Yes, "misery loves company" isn't a disaster recovery plan. For now, think of it like "nobody ever got fired for expecting a simple Google/Amazon/Microsoft service to work."
Hosting your own files in the cloud isn't too difficult either. My favorite service, and one of the first to arrive on the scene, is Amazon Simple Storage Service (S3). You just upload your files to directory-like areas that Amazon calls "buckets", and then reference the files using a URL that can be mapped to your own domain. For example, you might put a file named logo.jpg into a bucket named "images" in your Amazon S3 area, which you have mapped by DNS to files.yourdomain.com. Then to retrieve an image you'd just reference it with http://files.yourdomain.com/images/logo.jpg. If you need even faster delivery of content, you can use Amazon's Cloudfront CDN to geodistribute your S3 files -- even streaming.
Although most of these are relatively simple services and not difficult to integrate into existing infrastructure, they will still require the same sort of analysis and policy agonies that you'll need to consider for high-end cloud services like Azure. For example, how will you monitor the services to know when they've failed, and what steps do you take when they fail? Since many of these services are geodistributed, it's possible that your users in one part of the world may be having troubles when others are not. Services like Amazon's have status feeds that you can subscribe to, but it can take a while for problem reports to appear there.
In short, 2010 is the time to wade into cloud computing, not dive in -- the water isn't yet deep enough. This year, businesses of all sizes can take advantage of the basic cloud computing services already available. For more ambitious projects such as moving business-critical data into the cloud, 2010 should be spent experimenting with the offerings that become available and heeding the warnings of the pioneers who return with arrows in their back.