Dr. Mundo is a tanky top lane champion who is most commonly picked against teams which deal heavy magic damage (consisting of an AP top laner and mid laner). The reason Mundo is generally chosen against these teams is because it allows him to rush Spirit Visage, an item which was practically made for him considering the increased healing passive and the fact that all the stats which the item provides are useful on him.

Mundo has a relatively weak early game, but once he gets some of his core items he is able to tank insane amounts of damage and run at the enemy carries to chase them down one by one. A late game Mundo can become extremely hard to kill, especially if the enemy team lacks ways to reduce his healing and does not deal percentage health damage

(Hybrid Penetration Marks)
The magic penetration makes Mundo's abilities more effective as they are all magic based damage spells. However, Mundo does end up in a lot of close range trades as he needs to be in melee range for his Burning Agony and his Masochism also greatly increases his attack damage for a short duration. This makes the armor penetration extremely effective on Mundo as well.

(Scaling Health Seals)
Mundo is a health based champion: the more health, the better. The reason why I opt to use scaling health seals over flat health seals is because the scaling seals provide more health than the flat ones starting at level 6. This just makes the late game of Mundo even scarier.

(Magic Resist Glyphs)
Magic resist glyphs are pretty standard on most champions. Even if you are not laning against an AP champion, you will likely need them against the jungler and/or the enemy mid laner. There might be a super rare situation where the enemy team is entirely AD based: in that case using flat or scaling CDR glyphs would be great.

(Health Regeneration Quintessences)
These runes greatly help weak early laners like Mundo to survive lane. The health regen not only gives Mundo more sustain in lane, but it also helps him while casting abilities, because his health serves as a resource for his abilities.

There are a few different setups which can be used on Mundo, but they are all heavy invested into the Defensive Tree as his goal is to be as tanky as possible.

In this setup, the 5 points which are spent in the Offense Tree are mainly used to help Mundo in the laning phase. The cooldown reduction from Sorcery allows you to spam more cleavers, which is even more effective considering that Mundo does not use mana as a recourse. Butcher and Feast are strictly taken for laning as they will help you last hit as well as give you just a little bit more sustain.

Some of the alternatives to this setup are to spend all 30 points in the Defense tree or going 4/26/0 (only taking the cooldown reduction in the Offense tree).

While in a ranked game's champion select, if you pick after what seems to be the enemy top lane, make sure that if they counter you - you can play your best in lane and get the best items for that situation. For example, if they have a Darius - even though he does counter you, if you know Mundo will still be the safest pick, not someone like Teemo - pick him. Maybe if you build the correct situation items as shown above, like a Mercurial Scimitar for his passive, you can still carry/do well in lane.

Dr. Mundo is really useful for tanking out damage during a team fight. If you go in, close range against their AD carry, you can just stand there while your Sunfire Cape PROCs and the rest of your team bursts their team down. They will be forced to peel for the carry you are attacking, by focusing you down. But this will take a long time to do since you are really tanky o.o, so you can watch your team get kills again, and maybe pick up 1 or 2 yourself.

Pros:
1. Hard to gank, when he does get ganked and takes long to notice, he can use Sadism to escape.
2. Can farm from afar with Infected Cleaver.
3. Ult is really easy to spam after cool-down reduction, so not as many deaths.
4. Snowballs quite well.
5. You can take a lot of damage in team-fights without dying.
6. GOES WHERE HE PLEASES! =D
7. Nice Skins :S
8. Hard to kill, all the time.
9. Not really difficult to learn/get into.
10. <0.05% ban-rate (Patch 4.13)

Cons:
1. Doesn't deal a lot of damage early game unless you land some cleavers.
2. Ultimate is 75 second cool-down unless you get CDR
3. Uses abilities at the cost of health.
4. Can't eat people unlike Cho'Gath. :(
5. No AD Scaling (Excluding basic attacks)

Smite I think I don't need to tell nothing about it... if you jungling you take it, if not you don't.

Heal to get their usefull heal and Speed when in fight on early game. When jungling it's heal can be usefull to save teammates during ganks.

Teleport to can reach lanes and allyed troops fastly. It's good to gank/countergank and defend lanes.

Ignite or Exhaust if you want to focus to gank lanes when Jungling or playing aggressively on Top.

Flash it's onle valuable when laning.

Ghost it's very usefull to lane reaching and jungle cleaning.

Advanced Survival Technique

If you already play's with Dr. Mundo and know how anoying he can be when facing an APC/ADC or before buy Warmog's Armor, then you can use Flash or Ghost instead Teleport to avoid from this.