I should start by saying there are a number of different kayaking videos out there which don't necessarily fit into any of these categories, for many are quite unique and to lump every edit ever made into one of a finite number of genres would be doing the creator as well as the sport a disservice. With that being said, there are quite a few who possess similar if not identical characteristics, and for humor's sake, I'll be pointing out a few cliches, stereotypes, and examples that come to mind.
The GoPro Short Edit
Short, sweet, and to the point, GoPro edits are always good for quick entertainment. Especially if they have music and few to no breaks in the action, these can be fun to watch and surprisingly easy to put together as well. Though mostly (if not all) whitewater and little to no off-the-water context, you certainly get considerable bang for your buck. Here's an example of your stereotypical "GoPro short edit".
The Beautiful Edit
I wish I could think up a better name for this genre, but I suppose "The Beautiful Edit" does the trick--that's what it is, after all. I can see it now--subtle filters, slow-mo left and right, pristine water, slower music, etc. You know the type. This video and this video are my two personal favorites in this category.
The All-Too-Interviewy Edit
Senders. The whitewater content is absolutely epic; you can't deny that these guys are constantly pushing the boundaries of the sport. Their freestyle backgrounds make for some awesome downriver play when they aren't running the hugest whitewater in the world, but for Christ's sake, I don't want to watch you talk from your home office for four minutes before you get to the goods. Context is good, yes, but a whole self-guided interview is a bit much. Stick to the paddling.
The *blank* Tour Edit
Everyone loves a good post-trip wrap up edit. Cali tour, Chile tour, Ecuador tour, PNW tour, etc.--wherever it may be, it's always cool to get a quick look at much of the whitewater a region has to offer. If these videos don't make you want to get off the couch and go paddle in some other part of the world, I don't know what will. Here's an example of an instant classic in the "___ Tour Edit" category.
The Vintage Edit
Back when slicey boats were playboats. Back when Tao Berman absolutely hucked his s#%t. Back when people ran massive drops in 55 gallon boats. I swear that 720p made stuff look bigger. Here's a prime example.
The Documentary
These are typically longer, ranging anywhere from 20-or-so minutes to an hour or more. What I love most about these types of films is the context they provide. They go beyond the whitewater and give those who aren't familiar with the sport the context necessary to get a feel for the lifestyle and thought processes of extreme athletes. Here's the most recent documentary-style video I've seen--definitely worth a watch, particularly if you like the adventure factor of kayaking beyond what happens on the water.