Admittedly I haven't been able to play too many games since the season 3 patch came live but I've been able to play against, play as and observe several junglers to assess how they've been handling the new jungle. This is just a quick write up on those few junglers.
I also will include a little write up on the new champion Vi. I can't comment on her game viability. I can only comment on her jungle prowess as is before release and what has been observed.
I will also note which items I've been building the most and which masteries have been the most common that I've been taking.
Defensive masteries are OP and I've been taking them on everyone (except casters) at least up to 15 points. I get the damage reduction vs enemy champions which is dramatic on some champions like an Amumu with a doran's shield. With that said, you can tell I changed my masteries from the original ones that I had suggested. I am not a mathematician by any stretch of the word. That said - I've been taking combined masteries between offensive and defensive for bruisers or "tanky" assassins like Nocturne. The effects have been good thus far. Hell I've even seen supports dip into the defensive tree more than the utility tree. I'm sure they're going to nerf some aspects of it.
So far I've noticed (and discussed with others) that Wriggles champions are doing much better than the "spirit" champions. Any champion with any form of steroid that takes Wriggles is doing incredibly well. I know some will argue "but what about Dr. Mundo?" well we'll get to that in a second. In season 1, Wriggles was a very strong item and other items like boots or regrowth were considered gamble items. In season 2, Wriggles was pretty much overkill to the point where it wasn't needed by many champions - even those that would have taken it in season 1 - so the other choices became more attractive. Now season 3 is basically taking it back to season 1 where Wriggles is once again an attractive item and the power boost in clearing and sustain is very noticeable. Now that the jungle kicks your ass, you really do make full use of the item and you can visibly see it help your ass. The spirit stone is basically a philosopher's stone thrown into a machete and it doesn't really help you very much. It is basically a gold dump. It "helps" champions be a bit faster but the champions who are making best use of it are those that could have jungled before naked anyways like Maokai and Nunu.
As much as I hate to say it - and this is what I meant by him being a toxic champion - he's one of the champions that has benefitted so much from the jungle change. I hate Shaco so much but he definitely became a lot stronger and is terrifying once again. It was predicted that he'd tear other jungles apart now that they have a crappy item to start with and are at much lower health but Shaco has gained new recovery powers that he previously did not have. His boxes automatically attracting aggro (and fearing) have helped him not get his assed kicked by the jungle should he have fallen behind. Shaco is basically stronger against invasion now and he can actually recover. That's an annoying thought to the "find and kill the clown" strategy that was used to take him down. Also, like Maokai, the prep phase he has with the boxes pretty much makes it so he's one of the few junglers who can still have successful (whether kill or not) early ganks and not fall behind.
She's an AP with bruiser qualities. Yeah she's being declared as overpowered but as a jungler I think she's fair. She's gotten stronger more to the fact that everyone else got weaker and that the new items have been very beneficial to her. She's definitely seeing more play in the jungle. She managed to keep her incredibly versatility, her high health and speed unlike a few other junglers.
His versatility actually got shot. You have to build some offense on him right now in order to maintain what he used to have. This is kind of sad but it won't knock him out of being one of the more favored junglers. Just stick some more attack speed or make use of his strong AP ratios at least.
Some may consider him a "spirit" jungler but he honestly can take whatever item he wants. I've seen players just grab a cloth armor on him (with armor quints too) and grab a quick doran's shield and just farm all day. They don't even gank much - they just farm and stack ruby crystals which end up becoming ever item he wants. Dr. Mundo is still the fastest jungler in the game and, with health and armor stacking, will never need to go home. Of course he can still gank if he sees the opportunity but farming is the best option for him. Everyone fears a Dr. Mundo with a full item build who is close to unkillable. He is one of the champions who's a candidate for number 1 on the tier list.
While his clearing to "a bit" worse he's actually still a god level jungler. He can easily do a buff to buff clear still and then just look for other junglers to murder. He maintained his godly build versatility and his dueling powers and many others lost it. Aside from his first clear he's relatively the same. I overreacted I would say - plus he's a wriggles champion and that item is put to good use by him thanks to his passive and abilities. He's a candidate for tier 1.
Fiddlesticks and Warwick
Warwick didn't improve much. Yeah sustain is nice and all but he didn't get significantly faster and his ganking is still bad pre-6. To add to that - his level 6 ganking is strong but a lot of other junglers have strong level 6 ganks too. Fiddlesticks, on the other hand, did see an incredible boost of power and is one of the "spirit" junglers that strongly benefits from that line. Fiddlesticks can start with any item he likes or make use of the machete rather well (his auto attacks won't suck as bad!) and his subsequent clears got noticeably faster. He isn't likely to be a god tier but he felt stronger. It's up in the air whether or not his super sustain and supportive toolset will make up for him being fragile and vulnerable.
He definitely got stronger. He's another "spirit" jungler though admittedly he can jungle with any item he wants and still do well. His E helps him mitigate a lot of the damage from the monsters (which is rather noticeable). I would recommend buying a doran's shield on him to further increase the effectiveness of his E and that champion damage reduction mastery. To summarize Amumu's strength - he initially clears at the same speed but starts getting faster at a better rate compared to most other junglers. I don't even have to tell you how strong a farmed Amumu is vs an enemy team. His weakness vs duelist still exists of course so he still needs his manly bodyguards.
This one is a bit iffy but it is noticeable. He got much better as a jungler this time around though his build flexibility isn't as great as other junglers. You have to feed into both his offense and defense at the start with masteries and runes and then build some offense on him before you build defense. This is to maintain his clearing speed, which tends to be lackluster without. Otherwise he's become much faster after his first clear, the new items helped him out plenty and he is a Wriggles champion. His sustain has basically helped him replace other tanky damage champions and helped him become more attractive as a pick. He is likely to end up in tier 1 this time around.
Pretty much read the above for Xin Zhao except with less sustain but much stronger clearing power. In fact I think it's going to become a point that these two will be competing for the same spot in the tier list. They're similar in how their strength increased with an edge in different places over the other. Their ganks are both high damage and they both become incredibly powerful in the new jungle once they obtain a wriggles.
She's definitely much stronger if albeit still a really bad duelist. She needs as much cooldown as possible and her first clear is still fragile but then she just gets faster and faster. The buff to the duration of her W combined with full cooldown reduction means she'll have it up forever. She's likely not to end up being a tier 1 champion but that's because her "not actually tanky" issue has yet to be fixed but that translates more to team fights and skirmishes. As a jungler she's become much better but as a contributor to team fights - she's still as fragile as ever and it doesn't help that the spirit line doesn't make her that much tankier.
Now he's an interesting one to notice. His first CLEARS (not just his first) are noticeably worse than before but later they get much stronger. What changed though is that the new items basically give Hecarim a horse boner. The new spirit visage, the new boots and the spirit line (final items) are actually amazing on him. It's hard to say whether he's better or not because his early game got hurt but his mid-late game became even stronger than before. This one is up in the air.
Now here is one that people have been wanting to know about. He's one of the few potential jungler carries and I can easily tell you that he's even riskier than before. See his early jungle was always scary as hell and was easy to screw up. However, much like Hecarim, his early game became weaker and scarier but his transition actually feels a lot stronger. He is pretty much forced into a Wriggles position but that isn't so bad. The new items are amazing on him and he starts mowing down camps quicker than even Dr. Mundo and Shyvana. He's not the fastest initially (unless you are the god of Vegas) but he becomes incredibly fast and annihilates single targets. Much like Dr. Mundo - just farm up all day and only show your face when it's very opportune. He was always like this but now it's so much more beneficial that I did notice an increase in the power of my transition. Depending on how melee carries work - Jungle Tryndamere is feeling like a definite option.
Kind of the same deal as Tryndamere except with more desire to want to murder people. He just flat, all around, improved. Not much to say except that his weaknesses in season 2 became lessened, he became faster and can farm up - albeit not as well as junglers like Jax, Tryndamere, Diana or Dr. Mundo are. He's looking to be a very solid top of tier 2.
Aside from losing in the name department - she's actually looking to being a strong jungler. She does feel like she'd be a better laner though but, much like Riven, her jungling will still be considered a strong option. She's fast and maintains that speed, her sustain kicks in after she is able to keep her passive, and her ganking, while tricky, is definitely strong. She's set to being a very powerful duelist and definitely one that can tear other junglers to pieces if they were to run into each other. She even has wall hops and two gap closers! Let's sum this up - she has a few gap closers, high damage, strong steroids/debuff, a shield, AD ratios everywhere and strong clearing...she's looking to being a Tier 1 jungler.
I'm withholding the opinion of my favorite champion btw (Jarvan) as I still feel mixed about him. He definitely feels slightly better but seeing as I've always held him as my standard to compare all junglers to - I want to test him out a lot more.