There are two half-price same-day ticket outlets on the Strip: Tix4Tonight and Tickets2Nite. You get a bit less than 50% off on your show tickets from them, because you have to pay a $4 service charge, but other than that, these are bona fide 2-for-1 show tickets and the selections are generally extensive enough that it's worth your while to stop by for a look.
Tix4Tonight has more locations (at the Hawaiian Marketplace, a booth across from the Stardust, the Fashion Show Mall, and the Four Queens downtown); it also usually has more selections. The last time we looked, Tix4Tonight had 43 selections, compared to 33 at Tickets2Nite. Also, Tix4Tonight has a Web site where you can get a "sneak preview" of its top shows on sale that day (while writing this answer, we found half-off for the Scintas, Mamma Mia! and La Femme, and 20% off for Mystere; the Web site also has a printable $2-off coupon, so you save 50% on the service charge. Finally, Tix4Tonight advertises "last-minute tickets to some always-sold-out Las Vegas shows" at a smaller discount.
We did a big survey in April 2006 and found the following shows available at one of the outlets: Amazing Johnathan, American Storm, American Superstars, Anthony Cools, Avenue Q, Barbra and Frank, Bite, Buck Wild, Carrot Top, Chippendales, Clint Holmes, Crazy Girls, Dr. Scott Lewis, Erocktica, Fab Four, Fantasy, Fashionistas, Folies Bergere, Funny Business Comedy Club, Hairspray, Hypnolarious, Hypnosis Gone Wild, Jubilee, La Cage, La Femme, Larry Jones, Legends in Concert, Mamma Mia!, Matsuri, Mystere, Neil Diamond, Platters Coasters, Rick Thomas, Rita Rudner, Riviera Comedy Club, Scintas, Second City, Skintight, Splash, Tony 'n Tina, Tribute to Rat Pack, V, Vinny Favorito, Wayne Newton, World’s Greatest Magic Show, X and Xtreme Magic.
Obviously, a handful of these shows have come and gone, but this gives you a good idea of what you'll find when you go looking.
Now, if you have your heart set on one of the Broadway, Cirque, or major production shows, you should probably bite the retail bullet and reserve at full price as far in advance as you can. You won't find half-price tickets for shows that typically sell out or are never discounted, such as Ka, LOVE, Phantom of the Opera, Danny Gans and Tournament of Kings.
However, if you have an open night and decide to see a show, stopping off at a discount-ticket outlet and getting a twofer for whatever strikes your fancy at the time is an unbeatable way to go.