Keeping tires properly inflated on a regular basis will do tons for you. If you're riding in wet/rainy areas a lot, might want to consider getting an oil-based lube; wax lube is great for dry and dusty environments. Don't over-lube your chain. The various articles mentioned by others will give you an understanding of what to do, but basically, lube the chain enough so it doesn't wear too quickly, but not so much it attracts too much dirt and road grit.
Keep track of your miles in general and be aware of when it's time to replace bearings. You can learn to do it yourself, or have it done at an LBS, but just keep it in your mind that you should be doing that when necessary. (Part of this is actually learning where all the bearings are on your bike. Here's the list, in order of quickest to wear out--the hub of each wheel; the bottom bracket; the headset and fork crown; pedals.)
As far as brakes and wheels go, I'll only add to the above post that you should keep the rims of your wheels clean. If you get gunk or pad buildup on them, clean them with rubbing alcohol or mineral spirits.
Washing the bike at least once per season really helps, too. Wax it with car wax afterwards.
As someone else mentioned, store it indoors whenever possible.
Finally, if you hit any major potholes or bumps when riding, make sure to check if your wheels have been damaged or knocked out of true. Keeping your tires pumped will minimize this possibility, but if it happens, it's important to get the damage assessed sooner rather than later.
Remember that the parts of the bicycle are all working together, and if one part gets jolted, damaged or compromised, it could affect other parts. This is why, even if your bike rides fine after a crash or a bump, you should check it all over for any unnoticed problems.
As with all things in life, frequent assiduous but minor maintenance will save you time, money and headaches that inevitably result from basic neglect.