Las Vegas is perhaps one of the strangest cities in the world. At nighttime, the casinos are dark and the streets are lit up like daylight. It is a hyper-reality where pyramids, gondolas, Lady Liberty and Celine Dion meet. Tourists flock to the city immortalized by the Rat Pack, which is long, long gone ... But still, Vegas is a must-see because it is nothing like you'll ever see anywhere else.
Understand that Las Vegas is a year-round destination, so there are very small windows that are considered "off-peak" (e.g. cheap). Look for flights in July and August for the lowest flight prices, but beware that the cheap flights are due to the fact that this is the hottest time of year in Vegas. If you can handle temperatures up in the triple-digits and/or you plan to spend all of your time at the blackjack table, then this is the best time to go. Just make sure that if you venture outside, you have sunscreen and lots of water.
If you're not keen on experiencing heatstroke and you'd rather see some of the famous hotels on the strip (which is definitely part of the whole experience of Vegas), January and February is another good time to snag cheap flights. Lots of people go to Vegas to ring in the New Year, and most of them clear out the first few days of January. Keep in mind that many restaurants, stores, museums and banks are closed Jan. 1, the third Monday in January--Martin Luther King Jr. Day--and the third Monday in February--President's Day.
If you can book your ticket very far in advance or at the very last minute, you may be able to get a cheap flight to Vegas during any month. It's helpful to know that it is also usually cheaper to fly mid-week as well. If you're dead set on being in Vegas for New Year's Eve one year, try booking your ticket really far in advance (as opposed to the last minute). Also, if you're a tourist going to Southern California and you want to hit Vegas while there, it may be cheaper to simply rent a car and drive.