Apple's new iPad battery replacement service is actually an iPad replacement service. Apple announced this week that if an IPad requires service due to a dead or dying battery, it will replace that iPad entirely with free shipping. The service itself costs US$99.
Note that the battery must have died on its own accord; if you dropped it, spilled Mountain Dew inside or otherwise damaged the iPad in a way that diminished the battery's functioning, it's not covered. Also, the iPad you receive will not contain any of your data, so make a full backup before you send the defective unit off to Apple (and do a factory restore to remove all of your data if you're the paranoid type).
You can get the process started at an Apple Retail Store or Apple Authorized Service Provider. Apple says to expect the whole exchange to take about 1 week.