Infected Cleaver is very effective in taking out neutral camps. It deals damage based on enemy health, which neutral creeps tend to have a lot of. This allows Dr. Mundo to jungle effectively.
Because Infected Cleaver makes a distinctive splat noise and returns health when it hits an enemy, it can be used reliably for checking bushes for enemies.
Since Burning AgonyBurning Agony also gives you crowd control reduction in addition to the damage, don't forget to use it during team fights or while chasing/fleeing especially against crowd control heavy enemies. Also, the reduction does stack with Mercury's Treads to make crowd control very ineffective against Dr. Mundo.
A well-timed Sadism can bait enemy champions into attacking you even when they lack the damage to finish you. Force enemies to chase you across the map in their attempt to finish you off, if you can- sadism's speed boost combined with the cc reduction of Burning AgonyBurning Agony makes taking out Mundo frustratingly difficult.
After you reach level 6, you should rarely have to leave your lane. Although Dr. Mundo abilities use health, his Sadism has a fairly short cooldown so you can regain lost health about once every minute.
Due to a tendency for many players to counteract Dr. Mundo's health regeneration with Ignite, taking Cleanse as a summoner spell might seem like a good choice; however, it does not actually remove the healing debuff, only the DoT. It does combine well with Burning AgonyBurning Agony to cause strong crowd control resistance, though.
Since Sadism is a regeneration buff and not a heal it will give you the most survivability if activated right before you take major damage. Keep in mind the regeneration speed relies upon a percentage of your maximum health, so stack up for the fastest regeneration possible!
Frozen Mallet is also an excellent item on Dr. Mundo . It gives him extra health and the guaranteed slow. The slow from mallet stacks with the slow from Infected Cleaver, making him incredibly effective at keeping an enemy locked down with constant slows.
However, both counters lose their effectiveness if you build magic resistance. Mundo with Mercury's Treads, Spirit Visage, and Force of Nature will have around 150 magic resistance, meaning Madreds procs will only damage you for about 1% of your max health instead of 4%.
Another more risky route is to start Blue Golem without Smite (strong leash) → Enemy Red Lizard. Dr. Mundo has extremely fast clearing and very strong early 1v1. Depending on the enemy jungler's clearing speed, he can often steal Blessing of the Lizard Elder and wait for the other jungler, either forcing him to burn escapes or even killing him.
Using Spellvamp Quintessences may give you good sustain.