By plane
Salt Lake City International Airport SLC is the westernmost hub for Delta Air Lines, which offers nonstop service from 109 different destinations, most in the western US, but also from medium-sized cities in the central US and the large cities on the east coast. Nonstop service is also available from Paris-De Gaulle and 5x weekly service from Tokyo-Narita will begin in June 2010.
American Airlines, Continental, United, US Airways, and low cost airlines Southwest and JetBlue also serve Salt Lake City.
Cedar City CDC in central Utah is served with prop service to Salt Lake City, and St. George SGU in southern Utah has prop service to Salt Lake City and Los Angeles.
Canyonlands Field CNY serving the Moab area has service to Ely, Nevada ELY and Denver on Great Lakes Airlines.
By road
Take I-15 from Southern California and Las Vegas. It also enters from Idaho to the north, eventually connecting to Canada. I-80 connects west to Reno and northern California - the route begins in San Francisco. It also connects from Wyoming near Evanston, providing the quickest route from Denver to Salt Lake City. I-70 heads straight west from Denver, entering Utah near Grand Junction and providing quick access to the incredible desert terrain of southern Utah, although not to any of the urban centers.
By train
Amtrak (http://www.amtrak.com) runs the California Zephyr from Emeryville to Chicago, stopping in Green River, Helper, Provo, and Salt Lake City.
For more information, see Amtrak's website or Wikitravel's article Rail travel in the United States.