Where you stay on your trip to Las Vegas can make a huge difference, both in how much fun you have on your trip, and how much money you end up spending... or losing if you like to gamble, well you could win money but it doesn't happen as often.

Las Vegas Strip - It's the adult playground and the most popular tourist destination in the world. The 2.5 miles of road has dozens of incredibly large hotels (some of the largest in the world) yet it still fills up regularly. Where to stay depends largely on what you are looking for in your Vegas trip:

Business - If you're here on business you have a great boss. Chances are though you are expected to do a little work at least. If the rooms are paid for try to get one wherever business is expected to get done or in a nearby hotel and you can check out a Vegas map to find out what's where. If you would rather save money some Strip hotels that are a bit less expensive include Tropicana, Flamingo, Riviera (just off the Strip), Circus Circus, and Stratosphere.
Money Saver - As mentioned in the business section above, Tropicana, Flamingo, Riviera (just off the Strip), Circus Circus, and Stratosphere are your best bet for good room rates.

Party Time - Basically all and any of the hotels are made with this in mind, the hotels that tend to cater to a younger more rambunctious crowd include TI, Planet Hollywood, MGM Grand, Mandalay Bay, and Harrah's.
Luxury - Bellagio is still the most luxurious place to stay in Vegas. Others on the Strip include Wynn, Encore, Fours Seasons atop Mandalay Bay, and the Mirage to some extent though it has shifted to a younger crowd over the years.
Family - We're going to skip the "family" section for the Downtown casinos. Naturally they will all tell you they are family oriented if it means you'll pay for a room - but they're not. Downtown is for adults and we wouldn't recommend it if you have kids younger than say the mid-teen range. On the Strip some great places for the whole family include Circus Circus, Excalibur, and New York-New York. These casinos have games and other entertainment kids will love. MGM is right next to the largest arcade in Las Vegas and may be a good option as well.

Las Vegas Downtown - The downtown area is highly underrated. It has gone through a massive overhaul and refurbishing over the last few years and can really compete with the Strip now when it comes to entertainment. Viva Vision is by far the most impressive free attraction in Las Vegas, and to top it off you'll save a ton of money staying Downtown, even in the nicest of Downtown casinos, over the Strip.

Business - This is a smart move if you want to write off a vacation without spending a ton of money... er, we mean if you're doing business in Las Vegas. Rooms are less expensive downtown in general. The nicest hotel is the Golden Nugget. Other nice hotels include the Four Queens, Plaza, and Main Street Station. You can save some money at Lady Luck, Gold Spike, California Hotel, and Golden Gate; though you're saving money over the Strip at any Hotel you stay at Downtown.
Money Saver - As mentioned in the business section, Lady Luck, Gold Spike, California Hotel, and Golden Gate often have lower rates, and all of the hotels Downtown are quite a bit less expensive than the Strip.
Party Time - One of the cool things about Downtown is that every hotel is right there literally, so you really can't go wrong. The Hotels with Viva Vegas directly outside include Golden Nugget, Binion's, Four Queens, Freemont Hotel, and Fitzgerald's.
Luxury - While each hotel has its share of nice rooms and suits, Golden Nugget is the nicest Downtown by a long shot.

Las Vegas Hotels Outside of the Strip and Downtown Area - Yes, there is a Las Vegas outside of the major tourist areas, and there are even great hotels that are tons of fun far from the fabled Strip or Downtown. While most of these cater to locals, if you are looking for a great time in a more low-key atmosphere, or if you just like to gamble without all the noise and goings-on of the Strip and Downtown, check out some of these great places:

Las Vegas Hilton - About 2 city blocks from the Strip, home of an amazing sports book and hosting some of the most popular conventions in Vegas, the Hilton is always a very popular option.
Palms, Palms Playboy, and Rio - For all intents and purposes these can be considered "Strip" Casinos. They are literally right off the Strip on Flamingo. Both cater to a younger party crowd and mirror Strip casinos in every way except they happen to not be on the Blvd.
Station Casinos - These dot the entire Las Vegas Valley and almost always cater to mostly a local crowd. Some of the nicest include Red Rock, Aliante Station and Green Valley Ranch. Other popular choices are Sunset, Palace, Texas, Sante Fe, and Boulder Stations. Fiesta is also a lot of fun, there is one in Las Vegas and one in Henderson which is a suburb of Las Vegas.