Keep in mind this is not an actual tier list. Season 3 has not come out so this is merely a rough sketch of which junglers seem to show the greater promise. They are not lined up to show who is the best from left to right - they're just pooled into groups. The junglers in higher columns simply show more promise.
1. Skarner, Olaf, Nocturne, Dr. Mundo
2. Maokai, Nunu, Cho Gath, Lee Sin, Jarvan
3. Nautilus, Sejuani, Shyvana, Udyr, Darius, Diana, Fiddlesticks
4. Hecarim, Elise, Trundle, Warwick, Jax, Rengar, Xin Zhao
5. Zed, Kha Zix, Fiora, Cassiopeia, Master Yi, Malzahar
Just going to talk about a few of them with some more detail. Otherwise watch the video for explanations on more junglers.
Olaf - He's someone who became significantly more powerful with the machete that he actually ends up having better clearing time than before. Aside from an increase in his already godly speed the item changes will likely make a massive impact on him. Bruiser type junglers received a hefty amount of economic items that will help the jungler's early gold deficiencies. That said you also don't mess with a double buffed Olaf in the jungle and considering he's not only faster (and healthier) but the enemy junglers are a bit more messed up - he'll probably have a fun time looking for the enemy junglers.
Maokai - Everyone's favorite plant is basically the same thing. There is basically no need to worry about how effective he still is except if the game evolves around him. The only thing that can make Maokai less effective if the laner meta changes to something that can resist him or the jungle meta changes from beneath him.
Lee Sin - He only got worse enough not to be considered the god of the jungle. He is still very strong but it is going to highly depend on his ability to handle the jungle if he fails a gank. He's not a jungler that can idly farm the jungle. He will suffer whiplash from ganking early and failing because of how worthless the small camps are but he's one of the few junglers who makes quick work of the buff to buff camps. That said he'll be happy just hunting the enemy junglers and trying to murder them like he always has.
Nautilus - If you can believe it he feels a lot better. The machete item increases his damage against camps by a surprising amount and he clears rather quickly even against buff camps. He's still susceptible to being outright murdered by another jungler but hey we'll take what we can get with him.
Udyr - It doesn't feel like he's that much better. Tiger definitely feels stronger thanks to the machete and the new doran's blade but phoenix feels somewhat weaker. I think both forms will be fine though. I don't know if Udyr will make a comeback but I feel that he wont.
Fiddlesticks - He was fine in his first clear for season 2 especially after the dark wind buff. The problem was that the jungle began to scale in a way that he'd end up wasting too much time and mana finishing them all off. Now the new machete items just make sure he maintains his clearing speed. He still is a blue dependant jungler but at least now he's speed/clearing issue has been resolved.
Trundle - He doesn't feel any different and the only way he'd actually see play is if the meta changes. He excels vs teams with little to no tanks but as we all know most teams are chuck full of fatties.
Kayle - From what people have been telling me she has far improved in this jungle tanks to the machete. The other problems still persist in that she's rather flimsy at dueling in the jungle and that her runes have to be tailored for the jungle but she'd be able to fit the semi carry role from the jungle if she can manage it and if she's picked.
Shaco - Surprisingly he got better thanks to his boxes being stupid at buying him time and that now they aren't prone to just messing up and not collecting aggro. This apparently lets him do a buff to buff clear rather easily.
Gangplank - It's weird with him. He didn't get significantly faster (if at all) but his ability to use his parley against monsters improved. The small monsters take just one auto attack and bullet to the head in order to kill them. He can focus the big mob then when his parley is up he attacks the smaller monster and then Qs them to collect the increased gold. The ease in this will make it easier for him to achieve a gold advantage for his opponents and I'm easily excited to see how I can make this work.
Rammus - He got worse if you can believe that. He new jungle, even with a leash, kicked his ass and he cleared it even slower. Then they buffed him and I didn't bother to see if that made any difference.