What kind of graphics card is best for me?
The answer to that question of course is, "it depends." All other things being equal (namely money, which never is), there is no reason not to have a video card more capable than what you need. But since money is an important factor, you need to consider just what you do need, and make sure that you can get that much out of it at least.
E-mail and Web surfing
At the lowest end of computing-power usage are those who have very basic needs, such as productivity tasks like e-mail and spreadsheets. However, the proliferation of eye-candy on the desktop, and watching videos can still place moderate demands on the graphics.
What's needed: Most likely, a good integrated-graphics solution will serve quite well. However, a budget solution with a chip from a couple years back will provide some extra insurance at a reasonable cost in case needs start to change.
The casual gamer
Not a lot of time is spent playing games, and those that are played generally aren't the ones that place a lot of demand on performance. Also, the monitor isn't any bigger than 21 inches. A bigger monitor usually means higher resolution, which translates into more pixels for the graphics card to manage.
What's needed: Generally, a "midrange" card from the current or preceding generation of cards will have the best bang for the buck, while still providing enough horsepower to get the job done.
These are the people you always hear about. No amount of graphical-processing power can keep up with these demanding people, because before their demands are met, they've got a new game, or bigger monitor, and bigger demands.
What's needed: The latest and the greatest in the realm of video cards is always in demand for this group. Also, you may want to look at the options for dual-card machines.
3D Animation, CAD/CAM and video production
All three of these applications can benefit from good graphics support, but the emphasis is different. Instead of the raw speed of action games, image quality and pixel precision is paramount.
What's needed: A moderate- to high-power consumer graphics card can do quite well in this role for the hobbyist. However, more serious work will need a workstation-class card, such as the ATI FireGL line or the Nvidia Quadro.
One of the popular attempted "convergence devices" of recent years is the media center PC. This can range from a computer with a normal monitor that can receive TV signals, to a central media server that can send movies to the main TV itself.
What's needed: To receive TV signals requires a TV tuner card in addition to a graphics card. To output to a TV, check what kind of inputs your TV has, and what resolutions it can take. Then make sure that the video card you get supports a compatible output (your best bet is with DVI or S-Video).