Your Network Infrastructure Options
Most homeowners have three basic choices for moving data around their abode: wired ethernet, Wi-Fi, and HomePlug (powerline networking).
Nothing today beats gigabit ethernet for moving data around the home. (While 10-gigabit ethernet is starting to make inroads in corporate environments, it's still too expensive for most homeowners.) Gigabit ethernet translates to a maximum throughput of 125 megabytes per second, but you'll rarely see that speed; this is about as fast as a midrange hard drive, although networking overhead will make gigabit seem slower.
The primary standard for gigabit today is 1000Base-T, or IEEE 802.3ab. 1000Base-T runs over twisted-pair copper wiring. If you plan on using gigabit ethernet, you'll need Cat 5e (Category 5e) wiring. (You can also use Cat 6 cabling, though that's overkill for gigabit ethernet.)
Be careful when buying Cat 5e, however--some cheaper cables labeled "Cat 5e" may not be solid copper, or may be smaller than the standard 24-gauge, and your throughput on such lower-cost cables may be reduced. Make sure you buy cabling from a reputable manufacturer, and take care to avoid the cheapest cables.
The weakness of gigabit ethernet lies within its strength: It requires physical wiring. So you'll need to string Cat 5e to any room where you want that level of connectivity.
If you're running other kinds of wiring around the house (telephone, fiber-optic, coax, or the like), you might be able to kill two birds with one stone with structured wiring, which bundles all of them in a single sheath. The term "structured wiring" actually encompasses a range of products, including wiring panels, junction boxes, and other items, but I'm mainly discussing the actual wiring here.
While the structured bundle is thicker than individual cables, it makes running cable throughout a home easier, though you'll still have to punch holes in your walls.
In my home office, which is a basement room, I have Cat 5e running on the floor, in gathered bundles. This approach is fine in a single room that isn't intended for lots of visitors, but it's a less-than-optimal solution for social-gathering locations, like living rooms--you'll want to run the wires behind the walls there. (Check out SWHowto.com for more structured-wiring tips.)
If you can't (or won't) run cables through your house, the next best setup is Wi-Fi.