Taxis
Taxis in Cancun are easy to obtain no matter where you are. They are lined up anywhere a tourist may be. Taxi prices are standard - there is no bartering necessary nor is it welcomed. The best thing to do is to ask the concierge or front desk in your hotel what the standard taxi rates are. Many times hotels even post the rates because they are standard througout. For example, at the Moon Palace, there is a standard rate to anywhere in the hotel zone - it doesn’t matter if you are going somewhere south in the zone or at the top of the zone, or how long it takes to get there - the rate is the same.
Taxis take both types of currency, but it is best to pay in local currency so you don’t have to worry whether you are getting correct change. Often if you pay in American dollars, your change will be in pesos. If you are good at math in your head, you could figure it out, but if you don’t care, you can always pay in pesos.
From the airport to anywhere: exclusive-taxis charge non-negotiable US$40.00 or MX$400.00 (50.00 in the high season). Pay in any of the taxi stands inside the airport. You can take a collective taxi ("colectivo") for much less, you just have to travel with other passengers, and do a small milk run.
From anywhere to airport: feel free to negotiate, but expect about MXP$200.00 pesos
Taxis will not issue receipts, except if you buy within the airport taxi stand.
Downtown Cancun: cheap. Make belive you are a local, don't let the taxi drivers screw you over.
Rent-a-Cars:
It's better to rent a car or a scooter if you plan to move around a lot; it's cheaper than taxis. Parking is a pain in the hotel zone. When you buy gas, keep in mind that Mexican gas stations tend to overcharge (or undeliver) gas, i.e.: they tinker with the meter and charge you 10% more liters than what's actually delivered.
Other Options:
Bicycles, roller skates: in the hotel zone, there are some strips were you won't have any problem, but around "Punta Cancun" (northeastern point of the hotel zone) you can forget about it. The same applies for kid-strollers.
Walking: sure, why not....