Well, the gun that won the west has to be the Winchester model 1873. It was the most successful in a line of repeating rifles that started with the "Henry" rifle of 1860, continued with the "Yellowboy" of 1866, and culminated with the model 1873. All used a toggle link action that was invented by Smith & Wesson and originally appeared in the Volcanic pistol of the 1850s. Unfortunately, original Winchester model 1873's can be quite expensive, and Winchester hasn't made any since sometime before WWII. Uberti and Chapparal (sp?) make modern reproductions that are fine rifles. Get one in 44-40 (aka 44WCF), which was the original chambering of the model 1873 and is still a fine cartridge. Price will be around $800-1000.
The other major players in traditional "cowboy" lever actions are the Winchester model 1892 and the Marlin model 1894. The Marlin is still being made, and is a fine rifle. Get one in 44 Magnum, and expect to pay around $400-500.
The Winchester model 1892 has been produced for Winchester in limited runs by Miroku of Japan, and you can still find them around. They are excellent rifles -- stronger and more compact than the 1873. The Winchester '92 is the classic lever action of western movies, and it's the rifle John Wayne always used in his films. An excellent reproduction is the Browning B-92, also made by Miroku. Rossi of Brazil still makes the model 92, also. Expect to pay $500+ for a Miroku (whether branded Browning or Winchester), and $300-400 for a Rossi.
The Winchester 94 and Marlin 336 are the other common choices. The Winchester 94 was designed for longer cartridges like the 30-30, and it still excels with those cartridges. It doesn't work so well with the shorter pistol cartridges. The Marlin 336 is an improved version of the Marlin long action rifles of the 1890s and is also an excellent design. Neither of these rifles can claim the western heritage of the Winchester 1866 and 1873, however, or even the western movie heritage of the Winchester '92. I love the Marlin 336 in 30-30 as a deer rifle, and you should definitely own one, but if you want a cowboy gun, go with one of the classic Winchesters.