Does it hurt to have braces on?

99% no. The beginning of orthodontic movement will cause some discomfort, usually 4 to 6 hours after having them put on. The "pain" will be at its worst at about 72 hours, and then gradually lessen to all but none in the 2 or 3 days following the "worst" of the discomfort. Newer orthodontic brace design and advances in metals used for wires, have decreased the discomfort in orthodontics by a large factor.
Yes and no. The initial placement of braces is rather innocuous; however, as described by other doctors here, there is some degree of pain the next morning (so plan ahead, take analgesics before bed). Adjustment of braces at each visit will also cause some discomfort as teeth are moving.
Braces Don't Hurt! When the braces go on, you should have zero pain. Braces are glued on to your teeth and at not part of the process should hurt. It's generally 1-3 days following that teeth begin to be sore as they start the moving process. Orthodontists generally use very light wires to lessen the amount of pain during treatment.