Here are some basic jumps you tend to see pretty often. These should get you started. For (far) more advanced techniques, there is a nice list on the TF2 wiki.
Scout
Once in the air, can jump a second time. Easily done and can easily nearly doube the height or distance of a jump. Can also boost his jumping abilities with the following weapons:
Force-A-Nature This shotguns recoil can be used to boost a jump. For more details, see TF2 wiki for Force Jump
Atomizer With this weapon equipped (doesn't have to be out), the Scout can do another jump in the air. A "tripple jump", if you will. However, this will cost some HP for the final jump.
Soldier
This one you already mentioned, but for completeness sake I'll mention it here as well. The Soldier can rocket jump by firing a rocket at his feet as he's jumping. Extra height is gained by crouching while doing the rocket jump. Also, by aiming slightly further off center, the Soldier can control the direction of the jump. Requires some practice.
Once you get the basics down, also try doing another rocet jump off a wall. Mastering this technique will get you further away and to otherwise inaccessable places.
Demoman
Can use his sticky bombs to do a "sticky jump". Similar to the Soldiers rocket jump, but with stickies, but easier to do. Especially while running. Just fire a sticky to the ground, run over it, jump and detonate with right click. Once again, crouching adds to the jump and being a bit off center can give you more forward momentum. Also works with Scottish Resistance. Normally you would have to look at the bombs to detonate them with this weapon, but if the bombs are under your feet, it isn't necesary.
Engineer
The Engineer can "sentry jump", using the Wrangler that allows him to control the otherwise automatic sentry himself. It's quite simple, altough rather slow so it's rarely done in the midst of battle. Simply build a sentry, jump on top of it, take out the Wrangler and aim it upwards. If you're at the path of the bullets, they should propel you upwards. Can cause a lot of damage, especially if the sentry is high level, but can get the Engineer to some rather interesting places.
You should also remember that crouching during any normal jump can get you that last necesary inch of distance or height, since it will take a split second longer before your feet touch the ground.