Hardtails
No rear shocks. Generally lighter, simpler, and easier to maintain. Great for local riding.
Urban MTBs
Rigid. No front or rear suspension. Maximum simplicity. Shreddy.  Ride it to work. Pedal it to the trail. Shred some laps.  Cruise home. Sleep. Repeat.
Bikepacking Rigs
"Choose your own adventure" bikes.  Ya'll wanna ride Sheltowee next month? 
Freestyle MTB
Bikes for jumping