Opinions are mixed on this question. I'll give you my take on it. I have been to Las Vegas without a car one time. It was our second trip to Las Vegas and I doubt I would do it again. I enjoy the freedom of being able to get anywhere I want, when I want.
Don't get me wrong, we got around town just fine. We used the CAT busses, taxi cabs and free shuttles to get around and didn't feel trapped anywhere in town. However, we had to wait in 105-degree temperatures for the shuttle at the Hard Rock that was 15 minutes late. Fifteen minutes in 105-degrees feels like a VERY long time.
The CAT bus system in Las Vegas is wonderful. It's $2.00 for each rider and runs up and down the strip frequently. We never had to wait more than 5 minutes for a bus to arrive. However, often when they would arrive, they would be full of people. I don't mean that there wasn't a seat. I mean that the driver couldn't put more people into the bus with a plunger! At one stop I saw people unable to get off the bus at their stop because it was so jam packed!
The taxi service is also pretty good. You cannot hail a cab on the street, but there is usually a line of them at each hotel/casino valet area waiting to take you where you want to go. In my opinion though, the cabs get rather expensive. Each ride is probably about $10, depending of course on how far you travel, and just 10 rides would cover the cost of a car rental for a week.
I suppose that you have to make the decision for yourself. Where are your priorities? If that $100 for a car rental is going to make a big difference in your trip budget, I have some tips and hints on how to get around town for next to nothing.
CAT Busses are a decent way to get around town if you're on a tight budget. Rides on routes 301 and 302 (the Strip) are $2.00 per person. Or, you can buy 40 tokens for $20 and the ride is 3 tokens. Another option is the $30, 30-day pass. Click the link at the start of this paragraph for more information on routes, fares and how to buy tokens and passes.
Many of the hotels will offer a shuttle bus between their sister properties. You can often catch a ride from one general area to another. My favorite source of this information is unfortunately no more, but there is a great list on VegasMessageBoard.com here - Las Vegas Transportation Options.
If you're not interested in busses and haven't got the patience to wait for a shuttle, then this page has a great table for you. At the bottom of this page, you'll find a table that will give you the Taxi Rates from hotel to hotel, or from the airport to hotel. Which brings me to something else I wanted to mention...
If you aren't interested in renting a car, you'll need to figure out a way to get to your hotel from the airport. You can catch a transit bus from the airport to the MGM (line 108 I believe). But I don't think many people want to haul their luggage around on the transit bus. There are other alternatives.
Once you leave the baggage claim, you will see signs that are either pointing you to the rental cars, or to taxi/shuttle stands. Check out the Taxi Rates chart for costs from the airport to your hotel. Unless there are several of you, it's probably cheaper to take a shuttle. The shuttles cost about $3.50-$4.00 per person. Once you go outside the doors at baggage claim, you'll see a line of booths set up against the wall. Each one is a different shuttle company. There are several good ones, but I've had the best luck with Gray Line. Pay for your one way or round trip at the booth and they will tell you what bus to get on.
There's also the Las Vegas Limousine service that will take you to your hotel in a limo for $4.00 per person too. Another frugal and classy alternative.
Please don't hesitate to let me know if you have other tips for getting around town!