platformer games jumps are indeed quite abstract.
What I would worry about the most is wether the character will shift directions and how much while in jumping.
You say you've read several tutorials that describe actual mechanics of jumping (I would be interested in reading those if you can pass them on :p ) which has a lot of build up in taking impulse, this is what often gets reduced the most in platformers because we expect them to react quickly.
Look at the original prince of persia, tomb raider, flashback for examples that sacrified gameplay for proper buildup.
I may have misworded part of what I said, I didn't come across any tutorials, I just happened to notice a few short mentions of realistic jumping in unrelated topics, nothing exactly worthwhile though.
At the moment I'm trying to figure out the jumping for a characters that's generally similar to Mega Man in gameplay, though I have a total of 8 characters that I need to figure out. For a few of them I'm planning something along the lines of the flips found in Contra and Metroid though so those should be generally a bit easier.
I don't think I've played Flashback before but I have seen a few people mention it around here before. I have played the old Prince of Persia though, I remember seeing an interesting show on tv a long time back with the developer talking about how he recorded his brother acting out the jumps and such in person before making sprites out of it, they even showed a few of the recorded scenes.
Most normal platformer games just have the character fake impulse by raising either their legs or their arms or both, then trasition to heroic rising pose, then transition to heroic falling pose and a very quick crouching moment as they land (again to keep gameplay flowing).
This is pretty much all that is "required" but try to bring real mechanics of jumping if your platformer doesnt have too much wild shifting of directions, and try to accomodate the posing to your character´s particular personality. Other than this if you want more realism you can have different jumps for jumping backwards, jumping vertically and jumping forwards.
Those are some very helpful tips. Thanks!

Giving a character a more realistic jumping style might be interesting but it might be hard to balance out that character with others that have normal "game" style jumping, it's something to think about though. I'm generally going for a classic platformer with some ideas from a lot of the big ones like Mario and Mega Man.
I actually just tried a game recently that has some nice looking somewhat more realistic looking jump animations, the character has a vertical jump sprite and a horizontal one and it works pretty well. When you jump it uses just one rising sprite but at the height of the jump it transitions into a long animation for the fall, a lot of the time you don't see the full falling animation but as you fall further you see more and it kinda makes you feel like its a much bigger fall for the character. If you're interested the game can be
found here, i'm a big fan of the graphics in general, they look great.

http://www.zweifuss.ca/q/q.htm
you can check this page with SF3 sprites (click on a character, go to movement 1 and check jump u, jump uf, jump ub) to see how different a jump can be depending on each character's personality. This is also an example of the more involved aproach of doing a different jump for backwards forwards and vertical jumping. Do not feel required to have as many frames as these jumps, SF3 is famous for having crazy smooth animation
That is an awesome site! That should definitely help out a lot, lately I've been playing Smash Bros in training mode with the speed at its lowest and watching how different characters jump and move to get some ideas, having something similar to that on the computer is a big help.

Do you know if there's a feature on the site to watch the animations at a slower speed at all?