I have some issues with razor bumps and irritation on the front of my neck, under my chin. After a lot of research on face shaving sites, I have found that the more blades on the razor, the more chance of bumps and irritation due to the blades technically pulling the hairs and cutting below the surface. So some things I have read to try is go with the fewest number of blades that you can get a good shave with, and don't shave against the grain. I went from using a triple blade to a double on the face and only go with the grain on my neck. It has helped me a lot. My next step is trying a double edge or safety razor, which I have heard give good results for sensitive skin on the face.
Just remember that I'm talking about my face and neck, not my head. However, that advise probably will apply to the head as well. On my head, I use a Headblade with the Gillette sensor excel blades and go against the grain. I have never had any irritation on my head with that combination. And what Saint said is correct too, exfoliating is an important step to the shaving routine. I use a Nivia facial scrub and just rub it in with my hands.