The winds along the river and the shade of the trees while you are low in the ruins may lull you into a false sense that the weather is cool. If you climb up to ruins #39/40/40 and get into the full sun, you'll quickly realize how hot it is. Wear breathable clothes and bring your own water, there is none to be found in the ruins. Shoes that can handle a bit of mud and slick grass are recommended.
Toiletries and Medical Supplies: Particularly following any days of rain, the mosquitoes can be bad. Best to apply some repellant while you are on the boat such that you arrive in good shape.
Photo Equipment: If you want to take photos of the monkeys, better bring telephoto lenses.
Miscellaneous: One of the ruins is a small labyrinth, if you care to explore its short passages, remember a small flashlight.
Although there is not a lot of walking I would recommend tennis shoes. If it is rainning you will walk between a lot of mud.
Photo Equipment: It may sound stupid but don't forget to take enough film. Once you get to Yaxchilan you won't be able to buy film, there are NO stores to get some.