Apple has acknowledged a problem with time capsule devices released between February and June in 2008, where the devices will not turn on or will randomly shut down after starting up. This may cause hangs and other interruptions in Time Machine backups as well as other network activity.
In a recently released knowledgebase document, Apple provides a range of serial numbers (XX807XXXXXX - XX814XXXXXX) which may contain problematic components that lead to the power problems. If your Time Capsule is in that range, and you are experiencing these problems, Apple will replace the unit free of charge if you take it in to an Apple store or another authorized Apple service provider.
This replacement program will cover devices for up to three years from the date of purchase, so you have until June 2011 to get the device replaced. If you need to retrieve your data off the Time Capsule, Apple will provide some options to do so; however, you should first try to get it off yourself because Apple claims no responsibility for lost data.
UPDATE: This replacement program is not a recall by Apple, so if you have a working Time Capsule Apple will not replace it with a new one. Instead, the program is basically a warranty extension for a specific serial number range of devices, and will only be observed if your device has the symptoms described here. If your Time Capsule is in the range of serial numbers listed but does not have any symptoms, you will probably not have any luck getting it replaced. Likewise for if your device has similar symptoms but is not within the serial number range listed.