2003 225HP 1.8 TT with 50K miles.   I had an unusual hesitation problem that has been solved that I wanted to post so others may learn from this experience. 

Problem:  About once a month my TT would act like it ran out of gas when I was driving (usually taking off from a stop).  Engine would not stall but gas pedal acted like it was disconnected.  Reminded me of a plugged fuel filter.

I replaced the fuel filter but problem continued to occur about once every 2 or 3 weeks.

At the same time I noticed that occasionally my brake light would remain on after I parked the car and removed the key.   I had no idea that this could be related to the hesitation problem.

No check engine light present.

Solution:  I finally brought car to the dealer in Boulder.  They checked fuel pressure (OK) and decided to replace the brake light switch under the dash (near the break pedal).  It's been over 6 weeks now and the problem has not appeared.  Total cost of job was $60.  Apparently, the brake light switch can switch on making the computer think you are trying to stop so it cuts off the gas to the engine.  The system does not throw a error code in this instance.  This appears to be the source of my problem.  

I was very impressed with the dealer figuring this problem out and also with the fact that is was a inexpensive fix.