It's been a few years since I've been full time training at boxing, but my coach always recommended it. He was fond of a circuit training program, but he specifically liked heavy weights and low reps. Boxing and power almost go hand in hand and greater power is achieved through greater strength.
I'll speak for myself. I lift weights for quite a lot of years now . It made my punches stronger (a lot). Also weight lifting works well as injury prevention . My only sugestion is that you combine lifting weights with training cause if you dont you might loose some of your speed and explosion, because you'll feel hevier.
In this day and age weight training is a must. All sportsmen and women weight train whther they are footballers,swimmers or runners. If your boxing you obviously dont want legs like tree trunks so squats you can go easy on. Neck muscles you should definately train along with forearms,arms and shoulders.
I like a good mix. Boxing training, circuit training, and heavy weights (olympic lifts mostly) keeps the boredom away and keeps ya in great shape. But weights are very important.
joe calzaghe by the looks of most top class pro=boxers, they would appear to lift weigths, but interestingly i've read two interviews with joe calzaghe and he doesn't use weights because he says they make him too tight. whatever your own take on weights, i was quite surprised that a successful fighter like joe calzaghe was quoted as not using them.
mens health 'for a start, i don't do weights - they stiffen you up and for a fight you need to be flexible..instead i do the basic training that boxing has traditionally relied on' - Joe Calzaghe, Mens Health magazine, April 2002.
Depends how serious you are with your training and what you want to achieve from it. I'd recommend weight lifting regardless of what art you do. You don't have to do heavy weights... you can do light or medium to boost up your strength. But always combine your training with circuit training as well. Make sure you balance your training... such as training on legs as well as upper body and arms etc. If you're body is unbalanced... say your uppper body and arms are big and strong and your lower body is small and weak, it will be very unuseful as throwing punch can make you lose balance etc. Anyways good luck with it all.