Well one thing that I found to be really fun, if you want to drink is to do some sports betting. I'm a big hockey fan and we sat in one of the nice sports lounges, watched a hockey game and got free drinks for three hours because we had bet on it. (Sports booking area at The Wynn was the best)
If it's your first time ever, try to make it to both ends of the strip although the Luxor end had more casinos and newer ones as well.
Try to take in a show: you can buy tickets on the strip at these places the day of a show and they are pretty cheap. When I went, we saw The Scintas, they were really funny (and they are from Buffalo, originally so that was cool for me)
If you're going for something like an engagement, honeymoon, birthday, etc, tell the people as you check in. We went for my (then g/f, now wife)'s birthday and they sent us a few free bottles of champagne.
The bigger casinos all do something that's fun and free:
Stratosphere has the view, Mirage has the volcano and the white tigers, MGM Grand has a lion habitat, Bellagio does a fountain thing (i'd suggest seeing two of them, they do multiple different songs and some sync up with the music better), The Rio (thought it's off the strip) does like a showgirl type of party, with people with bright feather clothes and stuff, Treasure Island used to do a pirate show but i've heard they don't anymore, Caesar's has aquariums,
Go to a buffet. The buffet at The Rio is my personal favorite, but I've heard good things about other ones.
You might also want to check out Freemont Street. It's the original strip and it's got some cool stuff, like people doing street art and street dancing and stuff and there are late-night rock shows that are displayed on the canopy over the street.
Last but not least, find the Gold and Silver Pawn Shop from Pawn Stars, then let me know how it is because last time I went to Vegas I was unaware of the awesomeness of Pawn Stars