Formal:
* Don
* Doff (though this usually refers to taking off an item)
* Attire
* Vest (for putting on a vest)
* Gown (for putting on a gown)
Informal:
* Put on
* Slip on
* Throw on
* Dress (for putting on a dress)
* Suit up (for putting on a suit)
Other:
* Wear
* Sport (for putting on something you are proud to wear)
* Clad (used in a more descriptive way, like "He was clad in a suit.")
* Encase (for putting on a heavy item like a coat)
* Equip (for putting on a specific item for a purpose)
The best word to use will depend on the specific situation.