Maybe I'm crazy for thinking this, but I'd like to see a champion that has the ability to reflect damage, or to convert damage into healing...among other things...
Reflect Damage: Fiora, Rammus
Convert Damage into healing: Galio
Might make a cool support having several of those, however.
Also, I like to think of junglers as 3 main kinds, with slightly different names:
Ganking junglers: Alistar, Nautlius, Maokai Sejuani, ones with bad clear times and no invade potential that need ganks to work. If their early is ruined they lose.
Control Junglers: Fast clear speeds and/or good dueling to discourage invades, usually sub-par ganks. Examples include Mundo, Udyr and Shyvana. Farm junglers fall here too, as most of them are pretty fast with a Wriggles [Tryndamere, Warwick]
Junglers that don't really fit anywhere also go here [Trundle]
Invade Junglers: What it says on the tin, usually have slow-ish clears, decent ganks, and great dueling, and escape potential. Examples include Lee Sin and Nunu.
Generally Ganking beats Control, because of the lane dominance granted, the control jungler can't snowball it back because their ganks are poor, and can't carry late with their farm.
Invade beats Ganking because Invade junglers have good enough mobilty and ganks to help lessen the effect of the ganking jungler, while invading them and putting them behind so eventually they can't jungle at all. They can also shut down the ganker early.
Control beats Invade because most invaders can't beat control junglers 1v1 definitively, and this gets harder due to their fast clears, so they'll out-level. A lot of control junglers scale better than the invade junglers too, Shyvana and Mundo are far more useful late than a Lee Sin.
Some junglers are hybrids between groups. Lee Sin could easily be both a ganking and an invade jungler, based on playstyle.
Generally ganking junglers are most critical early, Invade is early but falls off slower, and Control becomes stronger as the game progresses.
If I had to split up the junglers:
Control: Mundo, Udyr, Trundle, Warwick, Tryndamere, Fiora, Master Yi, Karthus [These junglers focus on farming primarily, and have so~so ganks, at least pre-6. They are scary or very hard to kill lategame. Mundo dosen't die, nor does Udyr who stuns everything. Trundle too, as with Warwick. Trynd, Fiora, Karthus and Yi carry.]
Invade: Nunu, Kah'Zix [Love to go into the enemy jungle over anything else and steal/kill enemy jungler]
Ganking: Nautlius, Sejuani, Alistar, Maokai, Pantheon, Rammus, Volibear, Shaco, Twitch [Must gank and snowball lanes to be relevant]
Control/Invade hybrid: Shyvana [Will almost never gank, always farming and stealing jungle]
Control/Ganking hybrid: Olaf, Jax, Fiddlesticks, Skarner, Amumu, Diana, Malphite, Hecarim, Syndra [Happy to farm or gank, are not useless if they don't get ganks early, but can snowball HARD if they do. Syndra is like Jungle Karthus, except her post-6 ganks with ult are pretty scary... and she won't carry lategame]
Ganking/Invade Hybrid: Lee Sin, Rengar, Evelynn [These guys will only farm their jungle if there is nothing better to do or it is right at the start of the game]
Other: Shen [Focuses on Counterganking], Jarvan IV [Can happily do any of the three pretty well, based on playstyle, but is a jack of all trades master of none], Jayce [See Jarvan IV], Gangplank [Can do all three, but also has global Ult]
