My favorite thing to see in Las Vegas is free. Now I'm no expert on Vegas, so any recommendation I make should be treated with the knowledge that there are probably a million things I've never seen or done there. That said, easily my favorite thing there is the Fountains at Bellagio. As many times as I've been, I've never gotten tired of them; I could sit and watch them all night. I could post videos, but that wouldn't do it justice, because the experience can't be captured in a camera. Bellagio's fountains are a massive water show choreographed to light and music. I'm surprised how few people know that there isn't just one show (wikipedia lists 32 songs, though I don't know how complete their list is.) I was really glad when I took my pal Curt to see them for the first time and the show happened to be the one set to "Con Te Partirò," easily my favorite of the ones that I have seen. Find a spot close to the speakers embedded in the lightposts and railings, especially if during a crowded time. The fountains run on the half hour starting at 3pm on weekdays and starting at Noon on weekends and holidays. From 7pm to Midnight, the shows are on the quarter hour. (The last show is actually at 11:55pm. Fountains are also scheduled to run every 15 minutes from 11a-2:30p on Sundays during the Bellagio's "Fountains Brunch".) If you haven't seen them, make a point to when in Vegas, and stick around for a few shows - some are far better than others. You don't be disappointed.
[note: apologies for blog posts before June 2009 that may not be correctly formatted]