I've heard talk from some high end players that Shyvanna seems a lot stronger in Season 3, and she is undoubtedly one of the stronger counter junglers.

Noc/Shyvana if you like tank Surprisingly Rammus his clear is really fast and if you get caught just curl taunt and if they are winning ball roll out, and his ganks... Jesus the ganks.

I like Tryndamere because he can counter jungle but if he gets found just spin straight out of there and with his "w" he is relatively good at ganks takes a bit of practice but can be perfected

Ganking:
Lee Sin
Maokai
Rammus
Sejuani
Sustaining:
Lee sin
Maokai(his passive)
Nunu
Mobile:
Lee sin
Rammus

My conclusion: Even after the nerfs, lee sin is still good, but maokai is a better choice for starters.

Mundo, Xin, Lee Sin

Nobody has mentioned Olaf?

I think Olaf in general will be one of Season 3's highest picked and banned champions. Stacking HP and CDR on this guy is nuts. Pop your ultimate and ghost and just run towards their carries. I really like Olaf jungle because you max the Axes first, and the chase you provide with those axes is crazy.

Olaf has a great clear because the lower HP he is the faster his clear will be. Everytime you go to gank just pop a health pot. His ganks are great because you can keep picking up the axe and chase for days.

Late game Olaf is a one man army. Get around 3500 hp, 30% CDR and in team fights blow up their carries. He can't be stopped. Just last night I played an Olaf jungle where I went 13/0/15.

Udyr and Shyvana have the best clear times, but fall off late game.

Nunu and Warwick have some of the best sustain, but are relatively useless early game.

Nocturne and Warwick have the best ganking, but don't really shine until mid-to-late game.

Shaco is the best at counterjungling, hands down, but has the single worst late game potential out of every Jungle champion.

Lee Sin, Xin Zhao, Corki, and on and on are all viable picks.

Every single jungler in the game is the best in Season 3 if you know what you're doing. My suggestion is to just be careful in Champion select. In Blind pick you never know if you're going to be up against a Jungler that will rip you to shreds (Udyr and Shaco are terrifying Counterjunglers); in Draft Pick you need to pick a Champion that either counters their Jungle (if they get first pick) or can be easily supported by your team when they counter yours, and you need to know if your Team Composition supports the kind of Jungler you're picking. If the comp is a passive comp, choose a Jungler that can stay in allied Jungle and farm safely (Warwick is my preference due to his strong 1v1 skills and high sustain). If your comp is aggressive, pick a Counterjungler (I cannot stress how good Udyr and Shaco are at this). And always, ALWAYS do these two things:

Take Smite. It's invaluable for both counterjungling and deflecting the enemy jungler from doing the same. And:

Buy Wards. It'll prevent ganks, keep you in the know when the enemy Jungler is crossing the river into your territory, it'll let you know when the enemy is going for Dragon/Baron, etc. The support simply buys wards; you spam them across every inch of territory you can.

EDIT: If you're on Twisted Treeline, play as Warwick or Shaco. You will simply dominate the early and mid game, and if you reach late game, you'll be so fed that even Shaco can wipe the entire team.

Amumu, he just wants to be loved.

Shyvana still has really fast clear times and good damage. Her fast clear times allow her to be in the enemy jungle before they even finish their routes sometimes.

I prefer hecarim because mid game he gets his e with boots of speed and you can run over a single lane before they get back to the tower or ult for the fear so team mates can pick off kills