Personally, I do trim my cats claws as part of a weekly (or thereabouts) physical exam/checkover to make sure there are no hidden injuries (cats will hide illness/injury so that they do not appear to be prey).
However, I do still train them not to use their claws on me. The most basic method is to yell "owie" (some people will try to make an approximation of a cat pain noise, but just be consistent with whatever you pick) and then immediately stop play and leave the room. If the cat follows you, keep walking away from the cat (sometimes I have to shut myself in the bathroom) for 10-15 minutes.
If you are consistent with this, he will eventually realize that using his claws on you deprives him of your attention, and he'll stop.
You DO need to give him outlets to use his claws and hunting reflex. You should play with him using toys that distance your hands from his claws (so you do not get injured) and do not approximate hands (padded gloves with teasers on the fingertips are a bad idea). Cats are natural hunters and if you do not give a young cat an outlet for that energy, he will hunt your hands/feet/body.
I tend to adopt cats at about 2 years old, and they have terrible manners (which is probably why they were dumped at the shelter). At that age, we try to do a 20-30 minute play session each evening with lots of high jumps (Romeo, our current youngster, has jumped to my eye level!). Once they're worn out, we feed the gang dinner, and then they go right to sleep for the evening.
It will take a few months for your cat to stop using his claws on you. I recommend trimming his claws or using nail caps in the meantime if you're worried about injuries, but your "owie" yell will be more authentic if you don't ;-)