Time Machine is like version control for your life. It lets you restore files that you've lost or changed along the way, and does so in such a simple and elegant fashion that you never have to wonder "Did I back this up?" Time Machine just works. You hook up an external drive, set a few options, and let it go. Best of all, it's bundled for free with OS X.
That's not to say that Time Machine doesn't have pitfalls. It does. So here are a few tiny tips to help you make the most of your Time Machine coverage.
Local is not remote. The most secure way to protect data is to combine local and remote strategies. Time Machine is local, unless you have a really wide pipe to a remote location with your storage. If your house or office goes up in flames, the Time Machine drive connected to your system goes up in flames too. Not much to recover when your back-up is melty goo.
Consider using offsite storage, whether physically storing disks in a safe off-site location (especially if you're regularly rotating your Time Machine disks) or using a service like Dropbox or Amazon S3 to keep your data redundant. Offsite storage is an important component to full backup protection. Our Michael Terretta recommends Haystack's Arq service as a reliable and accurate (emphasis his) as well as affordable offsite solution. Steve Sande has had good luck with BackBlaze, and others recommend iBackup or CrashPlan.
It's not either-or. When you recover data from Time Machine, it always gives you the option of saving both the original and the restored version. As a rule, you probably want to do so, rather than accidentally overwriting, for example, your 30-page college application essay with the a few typo-ridden sentences of the first paragraph.
Think of file comparison as a Time Machine pep pill -- it allows you to perform more subtle restores to changed files. Apple's (free) developer tools ship with file comparison tools including FileMerge, opendiff, and so forth (not to mention our good old Unix command-line buddies cmp and diff). There are any number of commercial options as well.
You don't have to buy Apple gear. NewEgg and Amazon offer very reasonably priced external hard drives -- you can pick up a 2 TB drive for about a hundred bucks these days. Don't feel you must purchase an Apple-branded Time Capsule unless you really want to. Michael Terretta recommends the Western Digital My Book Studio line, because they ship pre-formatted for Mac, and have USB 2.0, FireWire, and eSATA connections. Mike Rose likes the additional fault tolerance of a Drobo, although you can get mirrored (RAID-1) standalone external drives relatively cheaply now.
Drives are not forever. Consider replacing your Time Machine backups every year or so. If your data is precious, then your investment in extra hard drives and offsite storage is a wise choice. I use overlapping backups for several months until I'm sure I can move the old drive off my system and not need it for any immediate restores. To do this, I leave the old drive attached but not set as my Time Machine drive. It's there if I need it; it's easy enough to re-establish that drive with Time Machine.
Not everything gets backed up. Time Machine automatically excludes certain folders from being backed up. Take time to open Time Machine preferences > options and review the exclusions you have listed. With multi-TB drives available, you may not want to exclude anything from your backups.
On the other hand, are you sure you want to back up your very large and constantly changing VMWare or Parallels virtual machine disk images? Almost certainly not. Add those to your exclusion list.
Other items to consider including are your Downloads folder (usually just things you can easily download again, often with more recent updates), IMAP mail folders from Apple Mail preferences (they can make Time Machine churn), ~/Library/Mirrors (Apple should have excluded this by default), /Developer (if you're a developer), and (more controversially) Application Support/SyncServices. This last folder stores your iOS backups, which can gobble up space when you're regularly using a couple of 32 GB iPhones and a 64 GB iPad. Personally, I do backup my iOS backups because I truly am that paranoid.
Finally, remember that you can exclude some items that are otherwise invisible, like your Dropbox database.
[Hints and tips on exclusions/large backups are courtesy of the excellent Time Machine FAQ.]
You can back up external drives. When planning to use your Mac (especially Mac minis and laptops with their fairly limited drive space) with external disks for storing media, be aware that you need remove those drives from the exclude list -- they are automatically placed there. If the drive appears grayed out in the list, i.e. Time Machine doesn't want to let you remove them from the exclusion list, like as not, they are not using HFS+ formatting. In such a case, you'll need to move your data to a compatible drive if you want Time Machine to keep that drive backed up.
You'll generally have to have the external drive attached (or a reasonable facsimile) if you want the drive to show up while browsing directly in Time Machine, but the files will appear (regardless on the drive) in Backups.backupd in each dated folder as a separate entry from your main drive.
Track your backups. CharlesSoft's Time Tracker (prerelease, hasn't been updated in a long time) allows you to track the contents of your Time Machine data, letting you visualize changes that have occurred since your last backup. If you know of any alternatives that provide similar functionality, please do let us know in the comments -- we're searching for good solutions ourselves.
Use wires if you can. As our beloved editor in chief, Victor Agreda, puts it, "Time Machine over Wi-Fi is like swallowing spiders every hour. Live ones." Ethernet and USB ports are there for a reason, particularly for an initial backup where you're copying thousands of files. If need be, subsequent backups can run wirelessly (although you'll be much happier with 802.11n speeds than a, b or g).
Just the FAQs, ma'am. Remember, there's a FAQ. And it's a good one (although unofficial). Look there for answers to mysterious questions.