(I thought this was good info & it wouldn't all fit in the "How to get around" box!)
Besides the always available free option of walking or the fairly cheap option of taking a cab, there are other ways to get around.
If you fly into McCarran, and you're not in a huge hurry and want to save a little cash: instead of taking a cab, go out the "Shuttle/Limousines" door (From baggage claim: the "Taxis" door is straight ahead and the "Shuttles/Limos" door is to your left, past the car rental counters)... and take a Shuttle to your hotel. For $4-5, Bell Trans Shuttles, CLS Transportation, Gray Line, or Star Transit will take you to your hotel on The Strip or Downtown. I also read somewhere that you can take a limo for $4 a person if you share with a group of people. We couldn't find any limos, so we took CLS Transportation. CLS also offers a "roundtrip" deal for $8. We bought it, but when we called to schedule the pick up, they told us that it would be at our hotel at 8:30 (3 hours before our flight), so we didn't take it. Looking back, maybe we should have, we missed our flight.
There are a few free shuttles: Fremont Hotel to Sam's Town, Sam's Town to the Stardust and the Fashion Show Mall, Tropicana Hotel to the Hard Rock and Palace Station, Hard Rock to the Stardust, Barbary Coast to the Gold Coast and the Orleans, Rio to Harrah's (A free shuttle travels from Harrah's to the Rio, and you don't have to be a guest of either hotel.), The Palms to the Rio (@ weird times), Stratosphere to the Starbuck's shopping center on Las Vegas Boulevard and Convention Center Drive.
There are also four free monorails/trams: Mirage to/from Treasure Island (runs between 9am-1am), MGM to/from Bally's (runs between 9am and midnight), Mandalay Bay-Luxor-Excalibur (24 hours a day), Bellagio-Monte Carlo (24 hours a day).
The bus (CAT)
CAT = Citizen Area Transit. It has 40 routes throughout Vegas. Most run from 5:30 AM to 1:30 AM, but there are 9 that run 24 hours a day. Fares are cheap... it's $2 to go from the strip to downtown with many stops along the way.