This Mundo build focuses on making you unkillable, as all Mundo builds should. Runes are debateable, since you could easily make a case for giving Mundo all straight health/health per level to support his passive, but I find that running without any Armor/Mag. Resist tends to make your health not as effective.

I go for Armor reds, Armor/level yellows, MR/level blues, and gold purples. "But Crimius, Gold purples are a waste of your Quints! There are soooo many other better choices, and it's not like Mundo has farming issues!" You're right, there likely are better choices for quints, however Mundos farming depends heavily on using Burning Agony in the middle of the minions, which until you finish Warmogs is going to get you killed. If you don't like my choice, use your own.

Pretty standard 0/21/9 tank masteries. You'll note that I opt not to take any points in Ardor, and instead go for filling out the third tier of the defensive tree. Ardor doesn't make you tankier, or improve your survivability, and those do. I also spec for Ghost, gold (moar gold), and incresed regen and xp in utility.

I only listed 4 items because those are really the major items in this build, everything else is situational. Start with the Ruby Crystal and make your way out to lane. If you have a jungler, try for the solo lane since the increased XP will make you even harder to bring down. Boots of Swiftness next because they can't kill what they can't catch, and being faster then they are is always a good thing. Some will opt for Merc treads, but I really think swiftness is the way to go. Combined with your ult and your ghost speed boost, you should be uncatchable end game if you find yourself in an overextended situation or a team fight that's killing you. After that, Warmogs is next so you can start farming it up for the extra health and regen, then Force of Nature to buff your regen even more. Oh, it has MR too. After you finish these 3 items, everythign else depends on how well you're doing, and what kind of damage you're taking. If you're doing well and aren't in danger of dying, grab a Leviathans and start stacking. Another option is Frozen Mallet, both of which are incredible health items that buff your regen even more thanks to your passive (you recover 0.3% of your maximum health every second). If you're getting nuked down by casters then throw a Spirit Visage down, or a Quicksilver Sash if you're being ignited (remember to use it). AD champs get thwarted by a Thornmail and an Atma's Impaler. Atma's is a good Mundo Item even if there isn't much AD on the other team, as it significantly boosts your attack damage based on your health.

Max Cleaver first. This is your ultimate harass and is absolutely amazing, so max the hell out of it first. Learn to land your shots, and you'll do fine. Remember early game that your abilities run off of your health, so if you're running low tone down the cleaver tossing a little bit. It also refunds half the cast price if it lands a hit, which is another reason to learn to land your shots. I try to take an early point in Machoism, and then Burning Agony, then really whatever I find myself using more, but cleaver first. Level your Sadism at the usual Ult levels (6, 11, 16) and use it for sustainability early game, since that's when you're at your squishiest, and if you're solo laning it can be tough to find time to leave your lane to shop.

Ghost/Ignite. Ghost with your ult will get you out of almost any situation, even if the entire other team is chasing you, they won't catch you. Ignite is a great finisher if you can't catch someone, and cuts the healing of those pesky lifesteal/spellvamp champs while it's active.

Other spells to consider:

Teleport: Gives you a better chance to leave your lane when solo laning, and can be spec'd in the first tier of the Utility tree. Always a valid choice.

Revive: Believe it or not, a tank like Mundo with Revive can be devastating. You hardly die, but when you do you don't stay out of the fight long.

Fortify: Solid tank spell, but I usually don't find myself needing it when I'm Mundo. If you want it, take it.

Flash: Always a good choice, but I find with Ghost and his Ult Mundo doesn't really need it. You should be able to escape any situation by running straight back to base.

Most Other spells could be useful in certain situations on Mundo (except Clarity), but Ghost/Ignite is the combo I've found to be most useful most often.

Early Game/Laning Phase:

You want to focus on harassing the enemy champs with your Cleaver, and staying alive. Check brushes with cleaver before the game begins, and by the time minions get there you'll be back to full health. Feel free to take their brush and harass them from there if they let you, even solo laning. Just know when to back off. Use your cleaver to harass the enemy champs when possible and to last hit minions, since odds are good the other team will zone you out of melee range. If you're lucky/unlucky, at some point they may try diving you, which is a good way to get a kill on one of them by landing a cleaver on one, igniting the other, and running away. You get damage on both, so if either dies then it's a kill for you. Use your ult to keep your health high, and wait this phase out.

Mid Game/Ganking:

By now you should have Warmogs and be on your way to FoN, if you don't have both already. You can now use Burning Agony to farm entire waves/pushes pretty effectively without worrying about the cost to your health. Your regen should also be high enough that your abilities are practically free casts. Farm your *** off when you can to make up for the poor early game farming situation. You should be going mid most of the time now, or wherever the other team seems to be focused so you can be a big, scary deterrent to them attacking.

Late Game/Ratpacking

By now you should be almost indestructable, building to counter the damage your taking and for health/regen where you're allowed to. If you ever feel threatened, pop your ult. It has a very short cooldown so you should be able to use it once every fight. In team fights, you basically just run in to the other team with Burning Agony on, throwing cleavers at the champs who run, mashing Machoism and autoattacking who you can, then pop your ult when you start noticing that you're getting hurt (most things will be minor mosquitto bites at this point). Ignite the champs that are likely to either get away or heal up in the middle of the fight. Warwick is a good ignite target, as are Swain or Irelia or Nocturne.

Here's the part that most tanks don't understand: you stay in the fight until either your team is dead or the other team is. If the other team is dead, congrats you won the team fight. If yours is dead then you can try to kill the people who are still left if it's only 1 or maybe 2 champs, or ghost away if you think you're likely going to die. 9 times out of 10, it will be the other team that dies because you cause so much chaos just by being there and by not dying when they hit you that the other team will run in fear (not the stupid ingame terrify mechanic, but the "oh **** we can't win" kind).

Your natural regen (even without your ult) at this stage in the game should be enough to where you only have to blue pill if you have gold to spend or you somehow found a way to die. Stay around the dividing line between the map you control and the other team controls and cleaver harass. Be cautious not to get caught, but if you do, then pop ghost and your ult and you'll almost certainly live to fight another day, and might even be able to stay after they stop chasing you to continue harassing.

The only counter to this build is when somebody applies an Ignite effect to you (like GP, Tristana, or Katarina have) that cuts your healing down. Quicksilver Sash is a great counter to this, since it clears all debuffs off of you, however that's the only real use for it (yes it has some MR, but there are much better MR items out there).