Do airplanes dump fuel before landing?
Is it true that they must dump excess fuel before they land?


Nope. You don't siphon your car just before your destination. Fuel is money.

Except in emergency in big planes, fuel then is a potentially lethal burden (weight).


  ... in case there's a problem with the landing and they need to abort?


Contingency fuel just for aborted landings, weather deviations, etc., is added during the fuel loading for such things. You get to keep it at the destination.



Further reading:


When are aircraft required to dump fuel for emergency landings?
Can a wide body airliner land safely with a full fuel tank?
Fuel planning—fuel calculation