Definitely take some of the tours. Especially to get away from the Americanized city and the tons of teens who now inhabit the city. I would recommend the tour to the Pyramids in Chitchen Nitza as a definite plus. Also take the ferry over to Isle Mujeres. A great island with good local restaurants for real mexican food. The beaches are less crowded and you can have some real private time.
I also recommend taking a day trip to Akumal. Excellent for snorkeling and about an hour drive from Cancun.
Many of the expensive tours can be done on your own by taking a reasonably priced ferry to another island or their bus system (similar to Greyhound) to Xcaret, Xel Ha or other points of interest. This will save you lots of money and you can experience the real mexican countryside.
Quick Tips:
The downtown flea market is the best for good deals. Also any flea markets outside of Cancun on the way to Tulum (in fact, the ruins in Tulum has a very nice flea market) or on the way to the Pyramids in Chichen Itza. But be careful, they belive all Americans have money so you have to really work hard to bargin down the price but this can be done so don't get dismayed. Also the vendors can be agressive so watch out.
Best Way To Get Around:
The public buses are a cheap and easy way to get around Cancun - 5 pesos. Taxis are good at night as they are very reasonably priced and easy to flag down, however, the buses are running all night, are very safe and come frequently.