League of Legends (LoL) Question: What 3150 champions are good junglers?

Gragas works the best for the current Enchantment: Cinderhulk meta. He is one of the best junglers out there so I would highly recommend him. Feel free to ask if you need in-depth explanation but I'd advice you to go with him.

Out of the 3150 junglers, I have to agree with divic, Olaf is a very solid pick, albeit he is a much better top laner than jungler due to the poke from Undertow (absolutely shreds all-melee champs like Volibear and Master Yi, eat axes all day) and the fact that he is nearly impossible to 1v1 due to the passive and the fact that his ulti ( Ragnarok) can get him out of situations as well as the long duration on the AD bonus. The true damage from his Reckless Swing works well against the tank meta, and his gets-stronger-as-he-gets-deader skillset is very good against slow, sustain-you-to-death tanks in the top lane like Sion and Shyvana.

Shen is also a good, versatile buy due to his massive tankiness and the fact that it's very, very hard to outright lose anything with him due to the easy escape from Shadow Dash. He also has a free teleport summ from his ultimate, Stand United, which can create a lot of kills from dashing right out of the ultimate, especially on top lane. Have your laner dive, ult, then taunt and finish off. This is quite effective at turning around top lane situations and possibly taking towers or forcing their jungler into a 2v1.

Other than that, Rammus is a good counter to AD champions because his kit demands armor stacking, and Soaring Slam can really affect duels. I do not recommend Nidalee because she truly has almost no tools of a jungler, no CC, a large amount of poke and lane control from Javelin Toss and Bushwhack, and her being squishy, even for an AP assassin. AP is not a very good choice overall for the jungle because everything an AP champion can do, an AD champion can do with no mana, and the usual advantages of AP (burst, range, poke) make no difference in the jungle and can often be a disadvantage. She does have a heal/AS buff from Primal Surge and some AOE clear from her Aspect Of The Cougar abilities, but this does not make up for her total lack of CC and farming ability.

Pantheon was very good around the beginning of the jungle rework due to the power of Enchantment: Warrior and Stalker's Blade diving him some very useful CC (however, the Warrior ench was nerfed around 5.2, and the tank meta just beat him to shreds). Albeit Grand Skyfall gives him good map control, he lost a large amount of his effectiveness when they removed his ability to early drag, a crown that is now held by Vi and Aatrox, who can level 4-5 and 3 the dragon, respectively. Panth was good, but is now beat out by the clear speeds and lategame of the hulk meta. Other than what's already been said (please don't try Mordekaiser jungle), I have nothing else to add (please, please don't be one of those kids that demands Urgot jungle.....do it for the children).

Olaf, Pantheon, Shen, Shaco, Nidalee, Mordekaiser & Gragas can all be played in the jungle, some need certain runes to function properly (mord / shen) but for the most part these can all be played as junglers.

If you are new then I'd recommend Olaf or Pantheon, these are both pretty straight forward junglers with strong jungle clear times. If you are quite skilled then Nidalee or Gragas could would nicely and if you want to try something different then Mordekaiser & Shen are quite unique yet can be quite high threats. Shaco is very versatile in the way that he can be played as a burst assassin, tanky disruption, split pusher or ability power one shotter, so it's too hard to say how Shaco is because it's highly dependant on the players skill and knowledge / experience.

• Shaco requires you to play a lot of it. It's either shaco main or no shaco at all. Shaco isn't part of any meta but still works.
  
• Pantheon is great jungler but not quite meta-champ anymore since cc-tanks are popular again.
  
• I do Not recommend Gragas
  
• Olaf is great counter to cc-tank meta mainly cause of it's ultimate and high amount of slows. I would recommend him. Great off-tank.
  
• Nidalee is popular jungler but dependant on hitting spears. If you are good on skill shots, Nidalee could be great.
  

Picking up these champions depends on your elo really.

Pantheon is great for lower brackets and rather easy to learn, but because of his rather linear skillset, you can easily be outplayed by players who understand how Pantheon works, leaving you unable to respond due to the nature of his skills.

Shaco is hard to learn to play, works very well in lower brackets, but is extremely difficult to play effectively at higher brackets. Also, because you bring nothing into teamfights as Shaco, you will have to snowball your lanes with ganks during laning phase or you simply become dead weight later in the game, where teamfights are more prevalent.

Gragas is more difficult to learn than Pantheon, not sure about his difficulty compared to Shaco, but he is currently either the strongest Jungler in the game, or tied with Sejuani. He was played very frequently in NA LCS as a priority pick alongside Sej, and has a very strong skillset, with good engage, slow, and gap closer with stun.

TL;DR

Get Pantheon if you're just learning the game/jungling, get Shaco if you want to try a different, unique, arguably more difficult style of jungling, or get Gragas if you simply want the strongest meta-pick jungler of the three.

Depends on how dedicated you are to learning curves. Shaco is a difficult champ to master, but it's pretty worth the trouble. Out of the three you mentioned, he really stands out because he's a special type of jungler, focused toward melting towers and early-mid game ganks. His main appeal is mind games, a skilled Shaco can really screw with your opponents and make them play inefficiently out of frustration. He's also really good at stealing dragon, since he can bwoop over the wall to smite, then bwoop back (bwoop being the sound you make when you use Deceive).
All-around solid champion to play but getting good at him will cause headaches.

Pantheon is quite easy to play compared to Shaco, good ganks and nice defense is interesting to deal with.

Gragas I'm not sure of since I haven't encountered him often, let alone in the jungle.