Dear Tim,
Your symptoms are consistant with a failed anti-dieseling solenoid. This shuts off the fuel to the idle circuit when you turn off the igntion, preventing a hot engine from running-on.
The solenoid could simply be unplugged. Check the connectiions.
Or it has stuck in the closed position (carbs need to be cleaned about every 30 months, on average).
Or it has simply failed. It is an 'always ON' solenoid and gets rather warm. Over time, the heat causes the windings to fail and the thing ceases to operate.
See any of the manuals to identify it. It may be replaced with the earlier idle-circuit jet (ie, no solenoid). But you would then have to learn to manipulate the brake & clutch so as to kill the engine when turning off the ignition.
To test it, simply connect it to the battery and ground the case of the solenoid. The plunger should withdraw from the jet with a CLACK!
cip1.com, that VW parts outfit up in Canada, carries replacements. See their on-line catalog. (Not very well organized, however.)
If the solenoid proves good then the problem is probably a blockage in the carbs low-speed circuit, fair evidence it's due for a rebuild. The kit is not expensive and the required skill-level is about on par with a bright nine-year old. You need some carb cleaner, solvent, compressed air (or a can of canned-air), something to protect the work surface (cardboard, newspaper, etc) and a few tools (varies according to the model of carb but basically a screwdriver and two wrenchs)
Instructions are in the kit.
Don't forget to use a new gasket when putting the carb back on, and don't bugger up the throttle wire -- hold the tip with vise-grips or similar when loosening/tightening the screw. The wires going to the electric choke and the solenoid deserve equal attention.
Service your oil-bath air cleaner while you're at it and if you're running an after-market air cleaner, it is probably the cause of your problems, having allowed dust/sand/etc to get into the carb.
There are quite a few other problems that could give the symptoms you've described, from a worn throttle shaft bore to a manifold or even improper timing... probably two dozen branches on the decision tree. But the solenoids are not very reliable (most guys replace them with the early style idle jet) and its failure has a higher probability than the other problems, most of which offer additional symptoms which you've not mentioned.
Good luck with it.
-Bob Hoover