I had that problem for a long time. When the mattress finally died (a spring poked through and stabbed me in the back in the middle of the night) I decided to go with a whole new bed. The one I had was a family heirloom and I didn't really care for the style.
I went to IKEA and got a simple wooden frame bed with very short metal legs, wooden slats, and a firm foam mattress - no box-spring. It's 100% completely silent.