I can't link you to videos but I'll give quick descriptions:
Free Riding: creative use of terrain and features. This form of riding usually entails big drops, big jumps, using everything from houses to trees to cliffs.Freeriders are the crazy guys of the mountain biking world. I would say that they are featured in more videos than any other form of riding as it is the most visually impressive. This is probably the most dangerous form of mountain biking. Competition normally focuses on impressive stunts and as such, freeriders do not "race." Freeride bikes are designed to be thrown off cliffs and can tend to be very expensive with crazy suspension travel lengths.
Downhill: The name says it all. Guys/Gals that like to focus on making it to the bottom of a hill as fast as possible. Often times they take ski lifts to the top of a mountain and ride down, seldom riding up hills. Very burly bikes, similiar to freeriders but the focus is not necessarily on style or stunts so much as making it down as fast as possible without losing control.
Trail/XC: Both "trail" and "XC" or "Cross Country" are the same thing, really. "Trail" riding tends to emphasize a more casual approach whereas "XC" can oten times imply racing. These describe general off-road riding where speed is emphasized over stunts but riding includes just as much "climbing" as "descending." Bikes are much less burly and prices for bikes are all over the map depending on one's needs. Trail/XC riding doesn't even necessarily need any sort of suspension system to still have a good experience.
All Mountain/Aggressive Trail: Incorporating elements of free riding into general trail riding/cross country. Bikes are a little burlier but are able to still climb hills pretty well.
Dirt jumping: Pretty much BMX minus the racing. This focuses on jumping dirt mounds and doing tricks in the process. Dirt jumping can be done using either a BMX bike or a mountain bike. The most common bike used for dirt jumping seems to be a hardtail mountain bike with a medium travel front fork.
4x: Kinda' like slalom skiing but mix in downhill mountain biking and BMX racing.
Cyclocross: A combination of road biking and mountain biking. Races include obstacles and it is common to have to "pick up and run with your bike." Cyclocross bikes look like road bikes but have beefier tires/components to handle moderate off-road riding. If road-biking is track and field, Cyclocross would be cross country running. Cyclocross races ride on grass a lot and do not venture into the woods a whole lot.
Free Riding: creative use of terrain and features. This form of riding usually entails big drops, big jumps, using everything from houses to trees to cliffs.Freeriders are the crazy guys of the mountain biking world. I would say that they are featured in more videos than any other form of riding as it is the most visually impressive. This is probably the most dangerous form of mountain biking. Competition normally focuses on impressive stunts and as such, freeriders do not "race." Freeride bikes are designed to be thrown off cliffs and can tend to be very expensive with crazy suspension travel lengths.
Downhill: The name says it all. Guys/Gals that like to focus on making it to the bottom of a hill as fast as possible. Often times they take ski lifts to the top of a mountain and ride down, seldom riding up hills. Very burly bikes, similiar to freeriders but the focus is not necessarily on style or stunts so much as making it down as fast as possible without losing control.
Trail/XC: Both "trail" and "XC" or "Cross Country" are the same thing, really. "Trail" riding tends to emphasize a more casual approach whereas "XC" can oten times imply racing. These describe general off-road riding where speed is emphasized over stunts but riding includes just as much "climbing" as "descending." Bikes are much less burly and prices for bikes are all over the map depending on one's needs. Trail/XC riding doesn't even necessarily need any sort of suspension system to still have a good experience.
All Mountain/Aggressive Trail: Incorporating elements of free riding into general trail riding/cross country. Bikes are a little burlier but are able to still climb hills pretty well.
Dirt jumping: Pretty much BMX minus the racing. This focuses on jumping dirt mounds and doing tricks in the process. Dirt jumping can be done using either a BMX bike or a mountain bike. The most common bike used for dirt jumping seems to be a hardtail mountain bike with a medium travel front fork.
4x: Kinda' like slalom skiing but mix in downhill mountain biking and BMX racing.
Cyclocross: A combination of road biking and mountain biking. Races include obstacles and it is common to have to "pick up and run with your bike." Cyclocross bikes look like road bikes but have beefier tires/components to handle moderate off-road riding. If road-biking is track and field, Cyclocross would be cross country running. Cyclocross races ride on grass a lot and do not venture into the woods a whole lot.