All WDW resorts have a dataport on each room phone. You'll need to have a internet provider with a local access phone number to connect your laptop, but there are plenty available (I use netzero). Cost is only .35 for each call (make sure it's a local phone number) for members and .75 for other guests.
OKW and SSR both have high speed broadband access for $9.95 for a 24 hour period. Bring a network cable or call to have one supplied.
If you don't have a laptop, you'll need to use a computer business center at one of the convention center resorts or the internet cafe at DQ - also for a fee.