Nobody is wrong at the point they say they are very good at jungle.
The avatar of the security and self-control of the jungle is warwick. He can start wherever he wants, and can do some kind of counter jungle.
The same for clearing speed is olaf. He's the fastest without any doubt. With Arm pen runes and maxing Q asap u get a 2 second cd skillshot with true damage which also slows the target. Awesome for early game ganks. Maybe he lacks at heavy CCs and you also depend on enemy overextension and ally's skills. Anyway is a must vs heavy CC teams.
The king of the jungle in versatility is Udyr. With phoenix clears the jungle very fast and has a good nuke for early ganks. His bear lets him ganks with success and escape from chasing. The bad point is that he's easily countered and his jungle routes are too strict. With his low mana pool and his abilities' huge manacost at early levels make him very vulnerable at counter junglers. Isnt too usefull for solo queues.
The master of ganks is shaco. As rammus was, he can easily enter a lane and gank whenever he pleases. Despite shaco hasnt a strong CC (boxes only last 0.5-0.75 at early levels) he has a built in slow with two-shiv and a teleport+crit skill. He hits harder from the back of the enemies so if they try to run away with a slow they will fall faster.
His potential shines on 1v1, 2v1, 2v2 and 3v2 fights.
At late game shaco usually loses his potential, specially on teamfights, where he has to enter almost at the finish because he's too squishy to appear on the middle of all AoE and CC that usually happens at that fights.
Trundle: He's getting very popular on high elo team setups. His jungling speed is above normal and he cant hold counter jungler fair easily. I wont coment a lot of this champ cause i didnt played it as much time as other champs i've written about on this post.
Nunu: well, if udyr is the king of the jungle, nunu is the king of the counter jungler. Actually he's nightmare of the enemy jungler if you play properly. With consume and smite can destroy any neutral quickly which allows him steal buffs, and destroy enemy jungle. He travels at amazing speed with his natural Mv Spd, W and lv1 boots, which he almost always starts with. U can get at the wraiths faster than the enemy jungle and smite the big one, kill all, etc. The fact is: if you dont kill all the camp, it wont respawn at the same time if you would clear it. That lets you the ability to reduce the gold and exp gain of the enemy what throws to the trash ganks, farm, etc. because he wont level up as fast as the duo lane, which is one of the aims of the jungler.
The bad side of nunu is that he becomes a snowball thrower and frenzy buffer at late game, what makes him a bit boring.
If you want fun: Shaco
If you want do it easily: Warwick
If you want speed: olaf, trundle.
If you want early dominance: nunu (he also can roaming with success).
U can check stonewall008's jungle tier list at reignofelementz.com to see more detailed version of this post.
If you wanna learn to play i encourage you to watch some videos/streaming from own3d.tv
Nunu: theoddone (this guy has good guides about nunu and olaf, check them out at solomid.com)
Shaco: reginald (he has also a guide with some videos at solomid)