Lee Sin will often invade lv 2 against any jungler who has a problem with their initial clear. Some like to invade your first buff, some will ambush you during your second (more commonly happening when your 2nd buff is your red buff). Good ways to deal with him are to have your support and adc ward the river just before or after leashing you, and if you see him coming, leave your buff with a ward in it and wait at wolves. If he tries it, you can often steal it and/or kill him. If he walks past it, he's on his way to you and you can either run or try to set up an ambush yourself.
Also, less known for counter jungling, is Diana. A core part of her jg is to ward up and play safe until 6 against any jungler with an easier time farming or dueling, but once she hits 6, she begins ganking mercilessly or counter jungling with extreme effectiveness. She clears fast, hits hard, and is great at setting up an ambush. If you are a jungler who still has clearing problems at lv 4 or 5, she may even invade you at your buff the 1st time it respawns if she can get the timer. Against a Diana, try to shut her down early yourself with invades or try ganking a lot to get ahead. If you are a devourer jungler, then i guess all you can do is ward up and call in mid lane to ambush her if she tries to get froggy.
Oh, and he's rarer than most, but there is Nocturne. At lv 5 or so he can start being pretty aggressive, and once he gets his ult he can gank or invade with it well, provided he has vision of his target. Idk how to counter that though.
Also: tips!
*Against a Shaco, have your top laner ward his Kruggs/Gromp at 1:10 in and check the buff. If no Shaco is found, you can try to start top jg and invade him, trading buff for buff. If he's not invading, you'll run into him at some point, so ward over the wall/behind his buff before starting so you can see him coming. Another thing to do is toward the bush at red/blue and start bot jg going Kruggs/Gromp ->Wolves/Raptors. you can do all of those camps without him seeing you, and your ward will let you know where he is so you can act accordingly. Sometimes, upon not finding you there, Shacos may just try to take the buff, and you can kill him for that if you play your cards right a lot of the time by ambushing him the same way he would've ambushed you.
*Evelynn has a weak first clear. Try invading her at her red. Regardless of what side its on, her first red will hurt her badly and she is quite susceptible to invades.
*Against Nunu try warding up and doing outer camps before buffs. If he invades, you'll spot him, and can often easily kill the immobile nuisance early on while he's still squishy.
*Against Shyv, have top laner/bot ward her buffs. Find where she stars and collaborate with top and/or mid and/or bot to take her down at her 2nd buff. This usually requires hard CC, but if you can control her jg and shut her down early, she'll spend quite awhile trying to farm up to usefulness. Don't let her. Keep her warder (have lanes help). If she goes cinderhulk, focus on ganking wherever she isnt, and then taking her camps (keep yours clear too if you can. If not, just make up for her invades with ganks). If it's devourer Shyv, shut her down early and be merciless. Keep tabs on her with wards and legitimately give her as few camps as possible while making sure to gank lanes so they dont try to aid Shyv. Once behind, she can only stall for lategame unless some hard throws happen.
Hope my comments helped. I may not be ranked too high, but I took my team to research this stuff awhile ago myself, and thats most of what I found.
Counter jungling relies on proper intuition. Predict where they started and assume where they will end up in X amount of time.
Fiddlesticks generally starts on the blue buff side, steal blue and he will have a hard time catching up.
Shaco has the fastest clear time. With a hard leash he can take 2 camps simultaneously and hit level 3 before the enemy even hits level 2. He likes to invade or gank super early.
The real Shaco has buffs around him.
Ward your camps when against Eve, she has to reveal herself when farming.
