THIS is so cool. Why take the extra fuel with you though? it's just a waste surely...

Wow how pretty! (commenting on the stars)
I agree I feel it is a waste though with the fuel...

Extra fuel is carried in case the rocket uses more than was calculated. The engines are shut down whilst fuel still remains as allowing them to run dry can cause serious problems including, potentially, the engine exploding. Indeed the very reason the shuttle has been delayed by a month is because of fuel level sensors giving false readings. These sensors are designed to cut off the main engines before the fuel runs out.

Fuel is dumped because in the past spent rocket stages have exploded months or even years after being placed in orbit. This causes debris which is a potential threat to other satellites.

Sweet.

Well, if i were in space, i"d like a bit too much juice than falling a little bit short !

belial,
What Waspie said (he's always right).

Basically, you never leave without reserve, in a plane, or on a rocket (and of cxourse, prudence would indicate the same thing in your car). With rocket engines, no reserve could mean a catastrophic end if fuel or oxidizer runs out prematurely (rocket engines do not like that condition...they tend to blow up rather than just sputter and die).

As to the dump, Waspie mentioned the possibility of an unstable reaction which might make everything go boom. Alot of times, a dump is precisely planned so as to separate the booster from the payload's orbit, to insure no interference. Often, a booster is maneuvered to an attitude which will allow a fuel dump to provide some modicum of thrust in a specific direction. When fuel is vented, there's always a change in velocity in some direction, which will change the orbit.