Cross country mountain bikes usually have less than about 4.5 inches of suspension travel. These bikes are built for efficiency, low weight, and self propelled speed. While they can handle most trails, they do not suck up the rough stuff as well as longer travel bikes.
So, if you want to win a cross country race, get to the top of the hill first, or if you ride ride on realatively smooth trails these bikes are for you.
All Mountain and/or Trail Bikes usually have about 4 to 6 inches of suspension travel. These bikes are built for more agressive terrain than cross country bikes but are generally slightly heavier. They aren't exactly cross country race bikes, but they are perfect for agressive trail riding as well as long epic rides.
If you are looking for an all around mountain bike that can take you almost anywhere without busting a lung, these bikes are for you.
Freeride bikes usually have about 6 to 8 inches or more of suspension travel. These bikes are built for abuse. Big drops, jumps, long shuttle rides, and other stunts are where these bikes shine. While most of them are still designed to get you up the hill as well, you will notice the extra weight.
If you want to spend most of your time in rough terrain, big drops, jumps, and manmade stunts, and you don't care how long it takes to get you there, these bikes are for you. These are also great bikes for riding the lifts at your local mountain bike park.
Downhill bikes usually have about 7 to 10 inches of travel. These bikes will suck up almost anything you throw at them, but pedaling up a hill can be quite a challenge. Downhill bikes are designed for high speed and highly technical downhill racing and little else.
If you think you might want to get into downhill racing, get a freeride bike. If you're really serious about it, a dedicated downhill bike is for you.