All/Any, if specifically mods. The server needs a mod plugin to run them, which they have none, so ones that add entities and items, like pixelmon, you can't use. Mods that improve gameplay, and looks, like optifine and shaders, are client side so them. Thats basically the types of mods. So yeah, all ;p
All mods are allowed. Just the ones that do add extra things wont do anything. btw, Mods, not hacks, just incase anyone things something.
Client side mods should work just fine. Note, there aren't many of them that aren't purely cosmetic. As Lopk said, no hack mods( aside from Nodus, and even then a lot of Nodus's functions aren't allowed).