Front and rear suspension is now commonplace on most MTBs you'll see in the shops and out on the trails. They've come along way since early models in the '90s, and are now light, efficient and inexpensive. Benefits are numerous, from increased comfort, higher speeds over rough terrain and better traction for climbing.
There are several different configurations available, from single pivot to faux and four bar, and more recently virtual pivot designs. Whatever the design, bikes are available in several different flavours:
Lightweight XC bikes: 3-4" travel, sub 25lb weight and steep geometry and skinny tyres.
Enduro/All-Mountain: Typically 5-6" travel, 30-35lb weight, relaxed geometry and chunkier build.
Freeride/DH: 6"+ travel (up to 10"), 35-45lbs, slack geometry, heavy build with big tyres and big disc brakes.