Although I'm not a jungler main, I can tell you some champs I've playe/seen played.
a list of all potential junglers i know:

If I would list them in categories of difficulty, it would be as follows, and some reasons (remember, my opinion).
Easy:
Amumu: Good jungle clears, easy ability combos, solid in all phases of the game, nice ganks.
Warwick: Easy clears, lovely in-jungle sustain, level 6 = definite kill on any gank.
Shaco: Easy buff clears with his boxes, no need for kiting, level 2 counter gank = first blood, free wards, good ganks.
Fiddlesticks: Stand there and press W to clear camps. meh ganks until level 6, good in teamfights, can solo objectives.
Vi: Her level 3 ganks are imo some of the strongest in game. good clear times. flexible build paths.
Tryndamere: Especially this patch, great sustain in jungle, auto attack reliant, E in, W to slow, Ulti for tower dives.
Master Yi: Aka lord right click. Camps are easy to clear, especially with your meditate to reheal, ganks are ok pre 6, nice damage, and literally right click to win.
Jax: Good clears, great ganks, strong dueler after 6, can carry REALLY hard.
Volibear: OP passive, tanky, good clears, solid engages and ganks at level 2-onwards.
Xin-Zhao: Good clear & sustain, gets right on the target, slow, knockup, great duelist.
Malphite: Probably the best level 6 tank, great ganks, good clears, naturally tanky, soem op burst too.
Aatrox: Great early game, good clear and sustain, good ganks, can go ballsy with his passive up.
Pantheon: Level 2 onwards can gank, blocks a tower shot, great early damage, nice clears.
Medium:
Kindred: Good to learn how to kite with, hidden op, late game damage is ridiculous, and level 6 allows for some solid plays if done correctly. Downside is her squishiness, and playing around her stacks to both get them, and benefit from kills by baiting.
Nunu: never actually played him in the jungle, but from what i've seen, he's a good counterjungler, has lockdowns at level 2, sustain in jungle, but difficult to get.
Wukong: Could be i never played him right, but his jungle clear requires kiting knowledge. His ganks are easy and strong, cause even with wards, if you camp a bit, then stealth in, they won't know you're there.
Ekko: He has lockdown, stun, and burst. Maximising his abilities in these ganks are where his difficulty comes in.
Gragas: Only reason he isn't basic is since his early clear is mediocre at best, his ganks are really nice. His ultimate is difficult to premeditate though.
Zac: Honestly, he's not difficult. Just work around his passive in and out of the jungle. His ganks are my favorite, he can tower dive nicely, and he has a nice passive. Really hard to get the hang of tohugh.
Sejuani: Really bad early game pre level 4. After that and some items becomes a ridiculous team fighter. Her ganks are op at level 3, but she's got difficult clear, and deceiving squishiness early.
Rammus: Slow clear times, and pre-items lacks damage. But his ganks arre nice, his taunt is especially lovely. can do objectives nicely with his low cd ulti.
Maokai: I've never tried him, but the best lockdown imo. Point and click lock down, 2 slows, tankiness, and great all-game. his only downside is like most tanky junglers is his early game clears.
Nocturne: Despite contrary belief, he's still good ganking pre 6, but at 6 they are ridiculous. The difficulty is he's prone to kiting and weak pre-lifesteal.
Nautilus: He's got good lockdown, and some of the greatest bulk in the game. Only problem is if you miss your one skillshot, your gank is useless, and potentially dangerous.
Olaf: Ridiculous damage, good clears, Good bulk. Problem is his Q is a lock down tool, so you need to use it as often as you can. Missing it = potential get away. Plus have to have balls to dive with your ult mid-late game.
Hecarim: great ganks, good damage, tanky. problem with him is his positioning.
Khazix: Some of the best burst in game on the AD side. Good ganks, level 6 = even easier ganks, good damage. problem: very squishy if you go full AD.
Jarvan: His E-Q combo is the only difficult thing. He breaks armor, deals good damage, great lockdown to force a summoner, and good teamfight presence. Just difficult to perfectly place everything, and is easily out juked by people with dashes and flash.
Nidalee: Reliant on the spear to hit for the ganks to be optimal, and she's squishy. Good mobility and great counterganker, and her ganks are good, but her spear is crucial to hit.
Shyvanna: She is ridiculously bulky, can go absolutely ham at level 6, but before that struggles.
Diana: useless pre 6, but after 6 gotta hit the Q. Great assassin jungler, good jungle sustain and clear, but the Q skillshot is odd, but required for a successful gank.
Udyr: Great clears, good ganks, only problem is you have to run to the enemy. aside from that, he's quite good, especially this patch.
Trundle: A lil difficult to truly get the hang of, and same for udyr in some cases, you need to run to get to the champion.
Nasus: He's viable in the jungle, and his slow is ridiculous. Problem is his Q is farm reliant, and he's just better in the top lane to optimize it.
Chogath: has sustain and good clear times, is naturally tanky, long range Q. He just requires his Q to hit.
**Hard: **
Lee sin: He is one of the best early game junglers, but his combo's are difficult, his abilities take knowledge to use to the best of your abilities, and late game presence difficult to find. Plus, skill shots, ward jumps... very advanced.
Elise: To really bring out her full potential takes guts. Her jungle clears are super easy, and her damage early is riduclous, and she is flexible in build path, but if you miss your coccoon, nothing you can do. Plus, you can always tower dive, but knowledge of her 6 abilities is crucial to master
Rengar: I would class rengar as difficult for three reasons: hard to really find a use pre 6, hard to clear jungle camps if not at the right skill level, and late game kinda has to be careful as to when and at whom he engages.
Reksai: She seems easy, her clears are good, her ganks are nice, early game power, global presence, but the difficulty in reksai is the micromanagement of your tremor sense and tunnels, and really maximizing your tunnels to excellent use.
Evelynn: Ridiculously difficult to micro manage her spikes all the time, REALLY squishy, and despite her invisibility, playing her without being busted by hidden pinks is crucial.
Skarner: His Spires have to be micromanaged, His lockdown pre 6 is difficult, his ultimate is single target and makes you vulnerable. with quicksilver sash however on your target makes him effectively useless.
Honorable mentions (also viable, but wouldn't recommend, either cause it's useless or just a waste of a jungler):

Hope this gives some insight :P