About halfway down The Strip there's a giant coca-cola bottle, you can't miss it. Inside the coke bottle there's a ticket office where they sell half price tickets for shows that night - so same day tickets basically. You have to get there early for the most popular ones (it opens at 10am I think) but you get given a priority booking pass for your next visit which puts you in a much shorter queue, gives you 10% discount, and gives you more chance of better shows.
We got half price tickets for pretty much all of the shows we saw which worked out really as two tickets for the price of one.
There are loads of free things to do all along The Strip too. The pirate show at Treasure Island is good fun. We didn't want to stand outside though so we went into the bar which overlooks the lagoon and had a drink while we watched it. The fountains at the Bellagio, the volcano at The Mirage, the gondolas (and singing gondaliers) at The Venetian, and the shops at Caesars Palace are all worth a look. Freemont Street is really good, it has a video screen overhead and on weekends there are street performers and musicians.
Siegfreid and Roy's Secret Garden at The Mirage is great, they have dolphins, lions, tigers, and other animals but you can get really close to them. We were sitting on the wall of the dolphin pool and one of them kept popping up and resting his head on the wall right between us, and there's literally a wooden railing and a chainlink fence seperating you from the big cats. The lions at the MGM are good too. There are often bands on at the Hard Rock Cafe and Casino and usually they're pay at the door and the clubs are amazing (if you're going without children anyway!).
There's so much to do, we were there two weeks and still didn't do everything we wanted to. Ask the staff at your hotel for recommendations and check out the Vegas tourism website, they have guides on there.