This topic contains answers to many common, general questions about Time Machine.
It does not, however, cover diagnosis and correction of specific problems or errors.  See Time Machine - Troubleshooting  for such help.
For questions and problems specific to Time Capsules, see Using Time Machine with a Time Capsule.  General problems with Time Capsules are covered in Apple’s  Time Capsule  forum.

Multi-disk backup
After having a terrible hard drive disaster back in college, I’ve been horribly paranoid about my backup arrangements. Mountain Lion will humor my paranoia by letting me use Time Machine to back up to several disks at once, automatically. And since OS X supports backup to networked drives, I can keep my files current in several physical places as well, without any extra work.

TimeMachineEditor is a software for Mac OS X Leopard, Snow Leopard and Lion that lets you change the default one-hour backup interval of Time Machine.
You can change the interval or create a more sophisticated scheduling (see screenshot below).
 
This is useful if you don’t need to backup every hour and don’t want the performance penalty. This is also especially useful if you manipulate lots of data within one hour as you would spend the whole day backing up.

One of the most useful pieces of Mac software I’ve ever come across is, TimeMachineEditor. As the name implies, it allows you to edit the interval in which your Time Machine backups occur. It’s free, and it’s super easy to use!

Time Machine works very well for automatically backing up your Mac, but if you’re backing up to a network drive, like a Time Capsule, your Mac and your network can suffer some performance hits while the backup is in progress.

Time Machine runs every hour, and Apple didn’t include a way to edit that interval. I deal with a lot of big files that change often, so the result is Time Machine was constantly running, and I was really feeling that performance drop. With TimeMachineEditor I’m able to change that schedule so Time Machine only runs twice per day… once while I’m at lunch and once in the evening. It’s actually extremely flexible, as it will allow you to define anything from a new repeating interval, to scheduled hourly, daily, weekly, and monthly times.

If you use Time Machine to backup your Mac, I highly recommend using TimeMachineEditor.

On Lion only, to make recent backups available to Time Machine users while travelling or otherwise away from their backups, Time Machine may make "Local Snapshots" hourly.
These snapshots are made only on portable Macs, and are kept on the Mac's internal HD (and on any other disks/partitions being backed-up) for a few days, space permitting.

While Time Machine gained a couple new features in Lion, I've just stumbled across one (so far as I know, undocumented) new piece of functionality in Apple's backup software that will have a lot of users cheering: You can now use a previous Time Machine disk with a new computer and inherit the entire backup history of the older machine. And it doesn't even require a flux capacitor.

With BackupLoupe you are able to answer questions like
Why is Time Machine so slow?
Why is my Time Machine drive already full?
Which files are actually being backed up?
Has a particular file/folder been backed up at all?
How many revisions of a file/folder exist in Time Machine?
A file/folder was deleted accidentally. When did this happen and where is the latest backup?
Is my backup drive big enough? Should I consider buying a larger one? And if yes, when?
In addition BackupLoupe provides intuitive ways to restore any item backed up by Time Machine to any location or exclude directories from future backups.