If you plan to stay on The Strip, the neon-lit world is your oyster. Monorails, mini-trams, cabs—everything is nearby and easy to find. If you're planning on visiting or staying anywhere else in Vegas, you're pretty S.O.L. The city is way too sprawled out, so don't bother with public transportation. Cabs take forever to arrive. Uber's a little better. Any way you look at it, you're going to need something on four wheels. Unless you're one of those crazy people that enjoys biking in 100 degree heat, in which case, do you.
Taxis are easy to come by all over the Strip, and a total pain everywhere else. Wait times can be epic. Las Vegas isn't a taxi-hailing town. Taxi drivers are ticketed on the Strip if they stop on the street, so don't be surprised if they drive right past you while you're flailing your arms around. There are taxi stands everywhere, though, so don't panic. Just walk to the nearest hotel or major attraction.
Uber and Lyft
When Uber arrived in Vegas well over a year ago, it wasn't allowed on the Las Vegas Strip. Signals were blocked, so you had no prayer of even making contact. Last Spring, despite protests from the taxi and limousine companies, the Nevada State Legislature legalized both Uber and its competitor, Lyft. There are designated drop-off/pickup points at airports, and like the taxis, you can't just order a car from anywhere on the Strip. Find a designated pickup spot.
The unfortunately named Deuce is probably the least expensive and most convenient way to travel along the Strip. The double-decker buses are run by the Las Vegas bus system (RTC) and run day and night making stops at almost all the major hotels. A two hour pass will cost you $6, but $8 will get you all-access for 24 hours. So spend the extra deuce for the all day Deuce.
Las Vegas Monorail
The Las Vegas Monorail runs adjacent to Las Vegas Boulevard, dropping people off fairly close to seven major points on the Strip. A single ride is $5 and a 24-hour pass is $12, so it's not exactly a bargain, but Nevada residents get a small discount at customer service booths.
Some casinos offer free trams between themselves and sister casinos. They don't leave as often, but it's a cheap way to get around.
Rent a Car
If you plan on doing anything AWAY from the Strip, just rent a car. Las Vegas is a sprawling city, and parking isn't too hard to come by.
A Warning About Parking
There are garages all over the city that promote free parking. These garages are only free if you're staying at the hotel, but they don't mention that in the fine print and will charge you outrageous parking prices. You're better off paying to park in a public lot.