Why do some airports have more than 2 runways, when LHR can get by with 2?
Heathrow is somewhat of a standout when it comes to volume. Your wording, that LHR "gets by" with 2 runways is apt. By movements, it is the busiest 2-runway airport in the world. By passenger volume it is second only to Dubai Intl. (Note, though, that DXB is home to Emirates, who has the world's largest fleet of A380's. They are the only airport that averages over 200 passengers per movement!)

Aircraft movement is the best way to look at it from a runway usage standpoint. The following chart is sorted by aircraft movement.*



As you can see, the top 3 all have 5 or more runways. There are 7 large airports with 5 or more rwys and they all fall in the top 16. The top 16 is rounded out by 5 airports with 4 runways, three with 3 runways and... LHR. The next 2-rwy airport on the list is Benito Juarez Intl. in Mexico City clear down at 21st on the list. 

Any busy airport with 2 runways has to make those runways work as tightly as possible with little room for error. Otherwise they end up with delays. If I sort the list by movements per rwy, all of those with 2 rwys rise to the top. 10 of the top 15 have 2 rwys. 



So, how does LHR pull it off? How do they manage to pack all those flights in to just two runways?There's a downside to handling that kind of volume with so few runways. The following collage gives a clue as to what that is. 



Those are just a random pick of arrivals at a couple of random times yesterday morning at LHR. There was no significant weather at the times. As you can see, you just don't arrive at LHR without being put in a holding stack. Every single flight I could find had to do at least one racetrack. At any point during the day, in places like Chesham, Effingham and Brentwood, if you look up there will be as many as 6 or 7 aircraft doing racetracks waiting to be cleared into Heathrow. That makes for very efficient runway usage when there are 20 planes waiting in line, but it's terribly inefficient for the airlines and passengers to have to spend so much time burning fuel circling around London.

On the flip side, building more runways has a down side too. It will get the planes out of the air quicker, but, as happens at Schipol - which has 6 runways - you can end up with a long taxi back to the terminal. 


All data was taken from Wikipedia.