Time Machine works best when you use it as it's designed: You simply let it run in the background and do its thing, only bothering it when you have to go back and get an old version of a document out. But if you ever want to do anything a little crazy with Time Machine ("adopting" a backup history on a migrated machine, for instance) it can be a little cranky.
For those situations, says researcher Simon Heimlicher, there's a cool little Terminal command called "tmutil." The command, which was introduced in OS X 10.7 Lion, allows you to reconnect your computer to older backups if you swap hard drives or upgrade your Mac. While Lion and Mountain Lion will give you the option to inherit old backups when you migrate your machine, it's nice to be able to do it manually if you need to.
It also allows for a few other functions, like combining and comparing backups, manually restoring items and adding or removing exclusions directly. Our buddy Cory Bohon points out a few more undocumented commands for checking your backup status. It should be noted that the improper use of "tmutil" could very easily munge your backups beyond salvaging, so be cautious.
If you use Time Machine quite a bit, especially in those crazy ways it's not always meant to be used, it sounds like "tmutil" is well worth learning about.