This is a guide to playing Rumble as a Bulky initiator/DoT. Preferably, you want to take solo lane top if you have a jungle, but also if necessary you can take mid and own, just with fewer double kills.

Also, knowing and understanding that even though the Equalizer is on a 70-90 second CD does not restrict it to team fights is very hard to grasp. In the span of time it takes you to B from lane and get back to the outer tower, half the CD will be gone. So, don't hesitate. Use it! It can save towers, help your team score kills, clear minions off of an overrun tower and cause an enemy to run a different route to avoid it.

Oh, and if you are looking at the Item list and seeing duplicates or weird slots, thats because its based on the game and team you are playing against! if they are all AP and no CC at all, obviously don't wasting time on Merc Treads. On the other hand, if they are all AP, a sunfire cape isn't going to go as far as warmog's and a force of nature.

This build will:
Take a lot of punishment
deal out an amazing amount of punishment
Shock the 2v1 top laners when you double kill them.
Cause you to be the focus(you want this, you are defensive)
Get you extremely in love with Rumble

this build will not:
Make you a pure tank
give you the ability to solo Ace the other team
Allow you to carry a team that is beyond carry
Extremely high offensive stats

For runes, I go flat armor seals and magic resist glyphs for the sole purpose of stacking up defenses early game. Defense is cheap late game, so no point in scaling. Magic Penetration marks are a must since 95% of the damage you will do(including in overheat) will be magic. Quints are kind of a toss up between more defenses or movement speed. I take defense, once again, because every defense counts in those first few levels. Movement speed I see as viable because every so often, a champion will outrange your flamethrower on a chase, wasting DoT.

Because of the new Masteries, you have 2 valid choices for Rumble. His solo lane/tankier option wiould require 9/21/0 with the 9 being AP, ghost mastery and the magic penetration bonus.

If taking Solo mid or a more carry-oriented role, build 21/9/0 with emphasis on AP scaling.

Tanky/Solo top: Take this first for the area damage and fear it instills in your opponent.
Mid/Carry: Take this 2nd but max first. Solo top/Tanky: Take this either second or third, based on who you are laning vs. Use it to snipe last hits if you are being zoned out or to help zone them out if you are winning the lane.
Mid/Carry: Take this first for minion sniping so you don't get overextended for a level 2 gank. Solo top/Tanky: Take this situationally 2nd or 3rd, and max it second. Great for absorbing minion splash or the one hit harrass you may suffer.
Mid/Carry: Take 3rd and use defensively or to retreat. Take at every level, and use to initiate a fight, or get someone low on life hugging a tower, among other things.

A few secrets that will both make your Rumble insanely cool, but also reveal to enemies of Rumble who read this how to shut him down:

Tall grass. Stand in it. Your opponent can not see your flamethrower. Re-read that. I don't care if they are standing next to you with 30 minions and you are roasting them all. They will not see a flame graphic at all or the source(you). This means? Stand in the grass and burn everything! They know you're in there? Burn them more! Chances are, they will assume you are too weak to do anything surprising so they will just stand around or continue to farm. But you are doing 30-150 damage A SECOND to them and all their minions while they have no idea. Then, pop out with a harpoon or two and the old Team America "Surprise, C*ckF*gs!"

Harpoon slow stacks. One hit is x slow. Two hits is 2x slow. Crystal scepter slow is applied each time you proc a flamethrower hit on them, making chasing -anyone- (except 'cannot be slowed' olaf/yi's etc) that much easier.

To realize Rumble's full potential, you have to first understand truly how he works. Everyone knows Yi and Tryn are crazy fast attacking, high-rate critting SOBs, and Akali is insanely high burst. But you won't see Rumble spike damage or drop someone in a second flat. He is, first and foremost, an AP DoT with huge survivability.

Early, he can stay in lane indefinitely with a regrowth pendant while he wears down any enemy champions that try to get free tower hits. The key is to make sure you continuously stay below full health by charging after enemies with flamethrower spewing, preferably in the danger zone. Your regrowth pendant will heal you plenty fast enough, don't sweat it. Eventually, you will hit 6, and then you win.

By level 6, you should have noticed the pattern the enemy champions take to avoid your flames and harpoons. As soon as they are at or around 300-500 health, get your heat to 30. Initiate by shield-boosting their direction and then slapping flamethrower. Before they react, drop the Equalizer across the ground where they habitually run through during your previous experiences. The amount of damage within an accurate ULT+flamethrower combo is close to 800 at level 6, +/-30% based on resists. Make sure you slap ignite on during the chase to ensure a kill, and hopefully a double kill.

After 6, build bulky ap/defensive items and lane until you see a gank possible. The Equalizer can quickly turn an over run tower into a kill or two, and once you have Ryali's Scepter, it is nearly guaranteed.