They are indeed called stationary trainers. Many manufaturers exist these days: Elite, Kinetic, Cycleops, Blackburn, etc. You can get them in versions with fan resistance, magnetic, or fluid resistance. The fan models tend to be the cheapest, though I don't think that many companies produce this type of trainer anymore. The fluid models are the quietest (wheras the fan can be quite noisy), but also the most expensive. Also of note, many of the magnetic and fluid models will also have a remote for the resistance adjustment that you can mount on your handlebars - rather than having to get off your bike to adjust the resistance on the unit itself.
You can purchase these at most bike shops, but I would call first. You can also purchase these online at practically all of the mail order outfits.
http://www.coloradocyclist.com
http://www.excelsports.com
http://www.cbike.com
http://www.performancebike.com
http://www.supergo.com
http://www.bikenashbar.com
Those are some places to look. However, if you do buy online, make sure the company you buy from doesn't have a retail (brick and mortar) location in your state - if they do, you'll also get dinged with sales tax. Performance, Supergo, and Bike Nashbar are the same company, and have retail stores set up in a lot of states.
Good luck.