Guns, melee weapons, armor and boots can all be modded once each. When you get a new level of whizkid, guns can be modded twice more and everything else can be modded once more.
Guns can have up to three of the same mod, all other items can only have one of the same mod unless you're specifically making an assembly, e.g. Tactical Boots requires two agility mods on a pair of boots which is normally impossible.
Most exotic items can be modded like normal. Most unique items can't be modded, some allow one mod in special circumstances, and I think only one unique item (Cybernetic Armor) can be modded like normal. All the mods have a page on the wiki saying what they do when put on weapons or armor.