As of the rework Lee sin is not the hard counter to Evelynn anymore! He might be able to see you but once he jumps on you and slows you just click W and run away from him. Evelynn trolls Lee Sin now, the tides have turned! And because of the rework on Hatespike you actually clear faster than Lee Sin does. Just keep in mind that you both like to gank early so be aware and watch for opportunities to counter gank. A good lee sin will still try to counter jungle you so make sure you get someone guarding your buffs to start out and then just be cautious in the jungle because he will out damage you early game.
Dr.Mundo is very annoying but not the most difficult to deal with. Mundo is stronger in a 1v1 situation so try to avoid confrontation with him in the jungle. Mundo is fast at clearing his jungle camps but at a cost, he jungles at low health if he does not gank early. A nice trick that has worked for me is that if you havn't seen him gank by the time you finish your wraiths, go to his blue because he will be at low health clearing his jungle and you can easily pick up first blood and the buff. Likewise, if you see him gank top with a red buff then you know it is safe to go steal his blue. Play smart and this shouldn't be a problem until he is unkillable late game.
Fiddlesticks is making a comeback as of his recent buffs (more damage to minions on E) He is not a threat to your jungle because he is a garbage counter jungler, but he is very strong in his own jungle because he will stay at full health the whole time, unless... you take his blue buff. Fiddlesticks is only good if he gets those blue buffs, limit his blue buff access and he will be rendered useless. If fiddlesticks gets a single blue buff then you are not doing your job!
Gangplank is relatively weak early and mid game. He will not threaten your jungle because he is not fast enough to counter jungle. Because he is so slow you can usually steal his red buff if you get a big enough leash on blue to save smite for his red. If done properly you can pull his red buff all the way to the brush on the other side of the wall so that you can take it undetected. Be aware late game as his passive will prevent you from stealthing, which is very annoying, and he will be very tanky with lots of damage.
Hecarim has very fast clears and stays at relatively high health throughout the whole jungle. Do not try to counter him because he clears faster than you and will beat you straight up. The most counter jungling the average Hecarim player will attempt is to steal your wraiths so make sure you get someone to stand watch so it doesn't get stolen early.
Jarvan is not known for his counter jungling so most of the time you will be safe, he might try to invade your blue however, Jarvan has very strong early game damage and if he catches you he is hard to get away from him. Best bet is yet again to just get someone to guard your jungle entrances in order to stay safe initially.
Jax can be very frustrating because if you build AD you can't hit him! He also has a great gap closer that will keep you from running away from him. On the bright side, you clear your jungle much faster than he does so this opens opportunities for some quick counter jungling such as the big wraith or the big golem, late game, wait to initiate until you know his counter strike is on cooldown, because otherwise you will do no damage to him.
The most annoying champion on the phase of the planet, ranged slow, ranged attack, splash damage, and the most frustrating ultimate known to man. She clears very fast and very safe, counter jungling is useless, I have yet to see a Kayle counter jungle but like always get someone to guard you. Late game she does a lot of damage and doesn't die easily, might be worth investing in an aegis early if she gets too fed.
Malphite is another annoying champion because he is known for countering AD based champions. Malphite will often rush for an oracles elixir and he is very hard to kill so you are going to have to play very safe against Malphite. Black Cleaver is a must because you need to reduce his armor in every way possible in order to get that Oracles off of him. He is very slow in the jungle compared to you but he remains safe and will most likely beat you 1v1 so I would recommend just clearing your own jungle and avoiding him if possible.
Maokai is very easy to counter and it is really fun to do. Maokai will begin to place saplings at his wraiths at 1:05 and wraiths will spawn at 1:40 so all you need to do is run in at 1:35 and pull his saplings so that he can't take wraiths, it is very easy to do, it is going to frustrate him extremely, and it will slow him down a lot. Maokai is easy to deal with and not that big of a threat, just play smart.
Master Yi is great at clearing his camps fast, but that is really all he is good at early game, he might invade your wraiths for a quick alpha strike but no more than that usually. Master Yi is one of the few champions you will beat if encountered 1v1 in the jungle so he isn't a big threat. Be aware late game however because he starts to hurt!
Nocturne is probably the most well rounded jungler in the game right now. He has good clear times, good ganks, good sustain. 1v1 you lose, and he is slightly faster in the jungle than you, usually you will both just sit in your respective jungles and clear peacefully. I havn't had much trouble with Noctunre personally.
Although Nunu is not the most common pick he is still frustrating if played by an intelligent player, have somone guarding red buff because he will most likely go in for a steal, in a 1v1 situation he isn't a threat because he won't do much damage early, he just doesn't die.
Whenever I see Olaf I smile =) Olaf will always start blue and and at red with almost no health left, take your wolves and blue like normal and then head straight to his red, he will be coming soon and you will be able to get a really easy kill this way, this rarely fails.
Pantheon is another really annoying jungler, he clears fast and he can't be killed 1v1. The good knews is he is bad at counter jungling, more bad news... he has a really strong invade so make sure you get your team to guard you so he doesn't come in for an easy kill.
Rammus is relatively slow in the jungle but stays very safe and can't be killed. He won't try to invade so this is a very passive match up. Be aware of taunt late game and try to initiate after it is on cooldown.
Shaco will try to set up boxes in your jungle to try to kill you, either in the brush by wraiths or by red buff. You need someone to guard red because he will try to steal it, in a 1v1 he isn't very scary because all he really has is his boxes. You really just need to be aware of him counter jungling you because that's what Shaco does. As long as you get people to stand watch early he shouldn't be a problem.
Shyvanna clears very fast and is deadly 1v1 she can easily steal your wraiths early so keep it guarded and just try to avoid her if possible. It is easy to counter gank Shyvanna because she has no escape and is relatively squishy early game, so if you see mid getting ganked and you are at wraiths, pause and go counter gank.
Skarner has very fast and safe clears and is pretty good at counter jungling, he will often try to start at your wraiths so like always make sure someone is guarding it for you. Don't try to 1v1 him because he will destroy you because he has built in sustain, a shield, and great damage. Black cleaver is a good item because Skarner likes to build tanky and needs to die before he rips apart your teammates.
Trundle stays at full health constantly and will easily beat all other junglers 1v1 early game. A good Trundle player will see and take note that Evelynn needs to start blue buff to jungle the best so he might try to sneak in and steal your red buff so make sure to keep that guarded early on and avoid 1v1 encounters and you should be fine.
Tryndamere is relatively similar to trundle, you won't be him 1v1 but he jungles at less health than Trundle, somtimes you might be able to pull off the Olaf trick because he may or may not be at low health when he takes his Red/Blue, most of the times they will start red but its hard to know because every game they do something different.
Udyr is pretty similar to Nocturne in the sense that they are both very well rounded and good at everything, 1v1 he will beat you and he clears extremely fast so just be careful and stay in your own jungle and stay away from him because he is annoying.
Warwick is easy to deal with because he doesn't do anything early game, he just farms his own jungle uninterrupted, he is very slow however and stealing buffs is very easy if you do it right, you can usually steal his red buff and delay him a bit. Late game, your hidden passive will really show, Warwick will instantly ult you as soon as you leave stealth, Guardian Angle early to counter him killing you.