I have an Audi in with the same complaint. I am cleaning the throttle body and relearning it. Check the MAF sensor readings and make sure cam timing is correct.

I recently had an Audi specialist change my timing belt & water pump. The car went from 13mpg to 18mpg with the timing belt change. So I knew my timing was not the issue. The rough idling was accompanied by hard starts after the car was warm. Both are gone after using Motorkote, well OK the rough idling has quieted down. I don't use the Audi recommended 91 octane petro. I use more affordable 87 octane and maybe that can explain away some of the idling but the recent sub-600 RPM idling felt like the car was going to stall. I consider Motorkote part of my automotive family now and in a few weeks will add it to my diferentral and my 5 speed manual trans.

It could be one of ten areas:

1) Air Filter - If the air filter is clogged the car will pull air in thru snow bypass door
2) Spark Plugs - I recommend a change interval of 10,000 miles/US and usage of Platinum multi-point plugs (2 or more prongs)
3) Fuel Injectors - Techron Complete, Motrokote fuel, or even ATF fluid work well to clean injectors. Just add to fuel tank before filling up.
4) Bosch Lambda / Oxygen sensor - 4cyl 1.8L has 2 / 6cyl 2.8L has 4x O2 sensors - should be changed after 100,000 miles/US. Usually the ECU will give you a CEL to indicate O2 sensor failure.
5) Clutch - Clutch could have wear dis-function usually occurring before clutch goes out completely
6) Vacume line disconnected or broken - recommended replacing vacume lines with 100% silicon lines after 100,000 miles/US. Replacing lines is the best way to find a leak.
7) IAC (idle air control/Stabilizer valve) - If you report idle problems to Audi, they will replace this item first but it is very expensive and often does not solve the problem. You can check and clean it easily.
8) Ignition coil packs - They have been known to randomly crack, bad Bremi coils have cause intermittent idle/stalling because sparks never make it to the Cylinder.
9) Throttle Body Dirty and/or mis-Alignment - Remove black air hose and clean butterfly. To realign or check alignment you need a VAG-Com. Watch Youtube link (www.youtube.com/watch?v=FVEz7it48s8)
10) MAF (mass air flow sensor) - the MAF rarely are the problem, but people focus on them because they do control rpm and fueling. Contrary to what the dealer tells you MAF's are cleanable. You should never touch the wires inside the sensor because of the oils on your fingers. Autozone sales a MAF cleaner spray and it works very well. Just follow the instructions.

If the car does start stalling I would:
1) Check for misfires - Using VAG-Com you can easily check for misfires (www.youtube.com/watch?v=2fyUyXgJMtY)
2) Check and/or Change - change my spark plugs to platinum 2 or 3 prong plugs and focus on the Coil packs, the spark plug wires, and inspect/clean the IAC (idle air control/Stabilizer valve).
3) Add 10oz of Motorkote oil additive just to ease the day-to-day stress on my engine. Motorkote really works sold at Meijer or Truck stops.