Before you say "Mundo Jungling? Wtf? NOOB!" think about it this way:

~ Mundo's cleavers deal a percentage of the minions' health so they're great for jungle. Mundo is considered one of the best dragon farmers at low level because of these.

~ His healing ultimate lets him stay jungling for longer and not have problems dealing with minions,

~ Razors are a must get to jungle with any jungling champion, Mundo's masochism is a good option already but with these and attack speed you'll get minions quickly.

~ A not so "tanky" build gives you the chance to stay at lower HP and make your Masochism skill stronger. This way you can deal more damage while ganking and the speed and attack speed boosts from this build will make you an excellent follower.

This guide will teach you how to jungle with Doctor Mundo

Skills

Adrenaline Rush - Dr. Mundo regenerates 0.3% of his Max Health each second.

Infected Cleaver - Dr. Mundo hurls his cleaver, dealing damage equal to a portion of his target's maximum health and slowing them for a short time.

Burning Agony - Dr. Mundo drains his health to reduce the duration of stuns and slows and deal continual damage to nearby enemies.

Masochism - Masochism increases Dr. Mundo's physical damage by a flat amount for 5 second. In addition, Dr. Mundo also gains an additional amount of damage for each percentage of health he is missing.

Sadism - Dr. Mundo sacrifices a portion of his health for increased movement speed and drastically increased health regeneration.

Summoner Spells

You can choose any spells you'd like to. There isn't really the need for smite or rally if you have all of the runes in this build and masteries complete. Even though, those spells help speeding up your early game. Heal is a great option for jungling at early game and staying longer in it. However, you should not be using Heal and Sadism together. Remember heal reduces the effects from external heals a few seconds after used.

Early Game

Early is the most important part of the match for jungling champions.
Start with a point on Infected Cleaver and heading directly to either lizard or golem. Which to start with is optional. You must be able to throw cleavers at the lizard/golem for succeeding at killing it. Start off by throwing a couple cleavers and meleeing it. At 2/5 of it's HP use smite (Cleavers go first since they deal more damage according to the target's current HP). Finish off the little minions with cleavers/melee attacks. Use your potion either while doing this or after depending on how you do against the minions. After getting your buff head to weaker minions like wolves. Right now you might be lacking HP and should have around 280~290 gold depending on how quick you dealt with minions. Go grab your Cloth Armor and get the other buff (blue if you took red and viceversa). Continue jungling until you hit 6. Go gank occasionally if anyone needs help. At lv. 6 your jungling becomes easier. Go back to base, get your Madred's Razors and get buffed again and then get dragon. Ult if needed and remember to use your smite. Go back to base again until you have enough for your Berzerker's Grieves.

Early Game Ganking

For ganking at early game your best choice is to wait at bushes until you have a good opportunity to cleaver the enemy and melee him with your Masochism. Use sadism to run back if you're being followed or turret is hitting you.

Fighting Other Junglers

Fighting other junglers as mundo is quite easy. Here are some quick tips for fighting them.

Master Yi: If you get to find him before level 6 and your HP is over half you should be able to 1v1 him without any problems. Start off by throwing some cleavers, pop up masochism and beat him. If you find him after level 6 though, try kiting him and landing a couple cleavers before hopping on him.

Warwick: Warwick, like Master Yi doesn't really have any chance against you at early game. Your cleaver deals more damage than what he drains with his lifesteal. Your melee damage while using Masochism should be higher than his even past level 6. So if you have around the same HP he does then he's no real challenge.

Fiddlesticks: Fiddlesticks is one of those you have to be careful of. Fear and Drain makes your job of killing him pretty difficult. However, when they're on cooldown he's an easy target. It'd be good to land a cleaver if you can before engaging. That way he won't be able to run away and you'll have dealt some decent damage. If he manages to use drain again just run out of range and for fear use some cleavers as soon as it's over.

Nunu: Before level 6n Nunu is a joke. He's no way more powerful than you and he can't really do anything that will hurt you badly. Just cleaver and follow him for an easy kill. After level 6 things can get tricky though. Just make sure you don't engage without enough health to survive his ultimate. A good thing to do is to stay back and cleaver him while you can. Wait for him to charge at you. His ult is on the way. Use yours to get out of it and then go back to him while throwing your cleavers. Finish him and if you've got over 200 HP remaining you're free to continue jungling.

Shaco: Shaco is one of the more interesting champions to fight in the jungle. Don't try to kill him. You are stronger and able to take him out easily, true. But at this point he will just most likely be able to run away and if you try following him you might aswell get ganked. If not, you will have lost your precious HP.

Malphite: Malphite might be your toughest opponent to fight. Make sure you break his sheild with a cleaver before he reaches you and then try to avoid getting hit with his ground slams. if you manage to evade both of these there's a kill waiting for you.

Udyr: Not to be engaged either. He is by far the most efficient and deadly jungler unless you can get him to make a mistake and run out of mana. If he goes on phoenix form he will most likely kill you.

Mid Game

Now that you have made it to mid game you are real strong and can 4-5 hit any squishy. By now you should have your Bezerker's Grieves. Now all you need to do is wait until you have the chance to cleaver. Then, run in and hit the enemy a couple of times. Ult if needed to catch up to the enemy or heal. Onve you have enough for Madred's Bloodrazors head back and everything will be even easier.

Mid Game Ganking

Very similar to early game ganking except for the fact that now you need your ult to be ready so that you can chase champions down and defend yourself. Also, if you have Burning Agony already you should turn it on so that you get the benefits from slow/stun time reduction.

Late Game

Now that you're at late game you should have your Bloodthirster and be ready to kill anybody with just a little help from your friends. You could get Malady or some other attack speed or critical strike item along with your Bloodthirster instead of Guardian Angel.

Throughout the match you should be able to drop anyone's health drastically with a couple hits and slow them while chasing to ensure a kill. Remind keeping you HP high and you will most likely be invincible. You can do this by healing yourself off minions at the jungle.

Directly taken from Teenaku's League Of Legends Wiki Vet Mundo Jungle Guide: http://www.leagueoflegends-wiki.com/lol/champions/dr-mundo/vet-mundo-jungle-guide---by-teenaku

I do not take 100% credit for this guide, it was made by Teenaku and edited by myself to get moved to mobafire for its commodities.