Chichén Itzá is one of the most famous ruins of the Maya culture on the Yucatan island. On its huge area you can discover a lot of artifacts in Puuc or Chenes style. Some of them are in pretty good shape due to intensive reconstruction and restoration.
Inspired by my imagination, I could nearly feel the spirit of this ancient culture, how they must have lived, prayed, worked and played at this place.
The wonderful main pyramid El Castillio dedicated to Kukulkan - a Maya feathered serpent deity - is about 30 meters high and consists of a series of nine square terraces.

I bet this is one of the most photographed pyramids in Yucatan. Unfortunately, you are not allowed anymore to walk up to the top of the pyramid to get an impressive picture of the entire area. My recommendation at this point is, to come early in the morning - when it is still not that hot - walk around and observe carefully not to miss the beautiful stone carvings and figures.
Detailed historic information about Chichén Itzá are available at:
http://en.wikipedia.org/wiki/Chichen_Itza

Another famous archaeological site, also surrounded by jungle, is Uxmal.
It is one of the biggest and most important cities of the Maya culture. A lot of restoration effort was invested to give us tourists a deep impression of how this pre-Columbian city might have looked like in former days. You can walk on sacbes (the ancient roads) connecting the different parts of the city. The most dominant buildings are the pyramid of the magician (highest building) and the governor`s palace.

The governor`s palace is a veritable goldmine of the Maya stone carving experience. You can find a lot of impressive, elegant and beautiful ornaments, figures and symbols there. The name of the city - Uxmal or Oxmal is quite interesting which means "build three times", but there is also a possibility that the name was Uchmal which means something like "what is to come". If you are hungry for more information have a look here http://en.wikipedia.org/wiki/Uxmal.

One of the smaller archaeological sites is Ek Balam. Nonetheless, it is one of the best places to admire the impressive stone art of the Maya culture and it is worth the entrance fee. By the way, the name Ek Balam means black jaguar. Even though the archaeological work started only in 1997, it has one of the biggest preserved buildings on the Yucatan island. Today, this building is called Acropolis, its ancient name is Sac Xoc Naj - which means something like white house of learning. There you can find some very nice ornaments and figures.