The once great Mayan empire left a number of historical sites spread all over the Yucatan. We had the luck to visit three of them: Chichen-Itza, Tulum and Uxmal.
Chichen-Itza (spelling varies, the Americans simply call it Chicken-Pizza) is probably the most touristic, daily organized tours take tons of tourists from Cancun every day to the site. Guides are available in English or Spanish and they will tell you about the ancient ball game of the Mayas and how they sacrificed virgin 13 year old girls on top of the pyramids to assure fertility of the land. With tons of tourists come tons of Mayan descendants trying to sell you silver and other handicrafts. Literally they emerge from every corner, with a “Hola amigo”, and after the fifth one it is really an effort to reply anything at all.
Tulum is also a very popular tourist destination. The site is smaller than Chichen, but since it is on the seaside, it is offers spectacular views. To stay on the budget side of life, you could use the exit to avoid the entrance fee, and if you happen to opt for snorkeling, go straight to the beach where the boats are, don't negotiate with any intermediate person.
Uxmal is much less frequented as it lays deep inside Yucatan, far from the touristic Cancun. However this is the only site out of the three that lets the visitors climb up on the ruins. I would definitely recommend Uxmal over Chichen, we had tons of fun in and around the ruins.