It could be timing or a bad distributor cap. There are other possibilities as well but those are the two best candidates. Check the Spark plug wires. I had the same problem and it was due to corroded rubber insulation on my wires. resulting in electricity arcing over to the engine! this was not good, but a change of the wires was all it took to fix it!
There are a number of reasons why your 99 VW New Beetle might be hesitating including overheating. Your Beetle might also have a leak in one of the fluids.
dirty fuel line
Hesitating is an adjective because it describes a manner in which someone was talking. Hesitating basically means lacking decisiveness or character or being slow in making a given move.
Not all moving objects accelerate. In general, an object will accelerate if there is a net force acting on it. For a ball in the air, this might be gravitation + air resistance; for a moving car (once you turn the engine off) it might be the force of friction; etc.
Asking your Volkswagon dealer would be a great start as to where you can test drive a Jetta wagon. In fact, the dealer there might even let you test drive a Jetta wagon there, if he or she has one.
If it simply dies without hesitating, I'd guess your crank sensor.
When you hear "he who hesitates is lost" it means that if you hesitate you may miss out on something. Somebody might take or get what you wanted because you hesitating in getting it.
you might want to check the relay.
YES DEPENDING ON WHAT MODEL THE 99 JETTA IS. THE LUG PATTERN IS THE SAME BUT THE OFFSET MIGHT BE DIFFERENT. A VW DEALERSHIP SHOULD BE ABLE TO TELL YOU WHAT THE OFFSET OF YOUR 99 AND YOUR 05.
the timing is most likle out your timing belt jumped have fun check sparkplug wires to be in the right order
Check the accelerator cable? It might have snapped
It might be your catalytic converter.