Seattle finally has light rail. Granted, it's less extensive than one might hope (one line) but it now reaches the UW, so getting to Capitol Hill, downtown, Columbia City and several south Seattle neighborhoods on the way to SeaTac Airport is fast and convenient. There is also commuter rail service which is unlikely to be of any use to you unless you live a fair distance north (Everett, Mukilteo, Edmonds) or south (Tacoma, Puyallup, Kent) of Seattle.
Another very nice travel option you won't use routinely is the Washington State Ferry System. King County's Metro bus system is extensive, and Seattle is considered one of the country's most bicycle-friendly cities. The UW home page provides info on the U-Pass and other options. Those who choose to drive to campus (and really, you'll be happier if you don't) can look forward to heavy traffic and expensive parking.