For some odd reason, I rarely ever see Rumble played in normal games. I've looked at several of the builds on this website and I'm beginning to see why. RUMBLE IS NOT A TANK!!!! Rumble is a super op mage. I've tried tanking with Rumble and I always lose. Therefore, getting Force of Nature is completely UNNECESSARY! (unless they have a ton of mages and you are getting beaten to a pulp by them. Still only put it in as an afterthought.) Rumble is a really weird character in that you can be running away from someone and then turn around and kill them in two shots. Just have to figure out when to turn around. He's an awesome pusher and harasser. His flamethrower can eat up champs like Cho'Gath eats up minions (and other champs.) His ultimate is THE ULTIMATE. It can be used to initiate fights, taking out half of the entire teams health. It can be used to last hit champs that are running away from a fight. It can be used to hit champs standing around drinking coffee near the turret. It is called The Equalizer for a reason. Well, actually, it more than equalizes, it nukes the heck out of the entire other team. That is only if it is used correctly though. I shall explain about it later on. Anyway, main point, I rarely play Rumble anymore unless I want a sure good game. He's just too cheap. My entire team can be doing poorly, and I'll come out with a positive k/d ratio. If my team is doing well, I'll come out with a stupefying 20-4 or something.

I try to go for a lot of early AP. I start out the game with around 20 AP. This allows my flamespitter to have an additional 10 damage per second which means that it is at 50 damage per second before I buy any items. That means that any squishy characters in my lane will be horribly harassed when I start picking apart my lane. (As a side not from runes, when you start the game, you want to spam your flamespitter. You will slowly build up your heat by increments of 5. You will be able to get to 50 before the minions reach your lane and even before the other champs get into your lane's brush.) This way you will get a 30% bonus damage on your flamespitter. You want to methodically spam your flamespitter such that it never hits 100 but never goes below 50.)

I go for a little bit of extra AP for later game. If I had the IP, I would make all of my seals instant AP for the above reason. But, this still works.

I get these runes so that during late game I can use The Equalizer without having to worry much about cooldown. During a standoff, I can sometimes get two of these shots off usually ending the fight and allowing my team to finish off the slowed and burning opponents. By the end of the game, the cooldown on The Equalizer is usually down to about 45 seconds. (After the nerf though... I'm not sure. I haven't played him after they nerfed his ultimate's cooldown and damage. He might just have become completely irrelevant, which would make me extremely sad. ;( )

Admittedly, Rumble has a great shield which allows him to be a rather good defensive character. So, my masteries are place to increase this defensive capacity as well as increase the amount of AP. I don't go for archaic knowledge because I can usually go for magic resist reduction using items such as Abyssal Scepter , and I like the extra experience from Awareness . It allows me to gain levels faster and level my flamespitter to do maximum damage faster. So, basically, I'm trying to hit Archmage's Savvy and Ardor . Other than that, you can decide. Just don't forget that Rumble doesn't have mana.

The items one chooses when playing Rumble are constantly in flux. It all depends on whether or not you see that the other team is getting magic resist. If they are then, you can pretty much throw away the above build except for Rylai's Crystal Scepter . If they aren't then, I've found that getting over a thousand AP is not such a bad idea... I've managed to build AP to the point where some squishy characters come towards me and start running away because they lost half their health in a second. Less squishy characters are more difficult to deal with but with a well placed Equalizer and a good team, you should be able to take down their entire team.
The main thing though is to rush Rylai's Crystal Scepter . You're entire team will benefit from you being able to slow down that pesky champ that ALMOST got away. When building, just remember that Rumble doesn't need mana. That means that items such as Archangel's Staff are more than useless to Rumble.

This is going to be very short.
is the BOMB.
Spam it, get minion kills, and super damage per second on champs.
It's great for harassing champs early game and great for slowing down an entire other team after get Rylai's .
Depending on whether your lane is starting to harass you, you should either try to build the shield or build the harpoon .
One level of the scrap shield is nice when jumping out of a bush to lay down some fire, i.e. Flamespitter or to allow you to run away or catch up.
One level of the harpoon is good for slowing down pursuing champs and catching up to champs that are running away. After one level of each, it depends on the game. But, the Flamespitter is the main spell.
As I mentioned, The Equalizer is THE ULTIMATE.
If you don't have predictive skills, this ultimate is somewhat useless (sort of like trying to use Ashe's Arrow without some idea of where champs are going.)
There are a few ways to place this ultimate. You can either click on the enemy champ and drag to where you think he might go. If a champ is pursuing a friend, you can click it on the enemy champ and drag towards the friendly. If there are several enemy champs in a small area, you can click and drag across all of them. If you know there is an enemy champ that is close to dying but he is in the dark, don't try to look at him. Just Ulti where you think he might be and drag away from any nearby turret. Depending on how safe he thinks he is, he will be somewhere along that line of fire.
As usual, you want to level the ultimate as fast as the game allows to produce higher damage output by the ultimate.
So... This wasn't actually as short as I thought...

I pick teleport and flash because I've already got a speed boost making ghost irrelevant, I've already got a continuous slow making exhaust useless, and I've already got a spell that can kill a champion after they leave the area making exhaust a pointless toy. I get flash because flash is just awesome. Flashing over some trees and pressing w is usually enough to get away. Teleport becomes extremely handy when coupled with a Teemo or a ward-happy team. Just teleport to a hidden shroom or ward and wreak havoc with The Equalizer.

Patch V1.0.0.120 ~ RIP the old Rumble. I hope this build still works. They didn't nerf the Flamespitter which is still your most powerful spell. Rumble packs a powerful punch. Used correctly his ultimate can be killer. Used correctly Rumble can destroy another team almost single-handed. Oh... Did I forget to mention what happens when he overheats, i.e. reaches 100 heat? He becomes ultimate pusher Rumble! His innate ability allows him to deal 20 + (5 x level) + (0.35 per ability power) magic damage for 6 seconds. I usually use all of my abilities as fast as I can, except for The Equalizer which doesn't produce heat, to overheat when hitting a turret. (Someone's going to have to correct me if I'm wrong about this...) Anyway, it's great if you've overspammed your abilities accidentally.
Overall, Rumble was awesome in the right hands (i.e. mine). I'm not sure if he's still awesome but I'm going to give him another go as soon as I master a few other characters. (Still crying over Eve nerf...)