I'm a bit new to the whole field of microcontrollers, so try and spare me any potentially befuddling specifics.
The short answer is "all of them" (probably) and the long answer is "what do you mean by compatible?"
If you have some suitable hardware that can output appropriate digital or analog voltages, then you can communicate with whichever microcontroller you need to communicate with.
If you're want to use something like an Arduino, consider what is supported by the LINX package or similar.
Do you mean what microcontrollers can be programmed natively with LabVIEW?
Using LINX (Free) Adruino and a few others are supported.
Using the Arduino Compatible Compiler for LabVIEW by Aledyne-TSXperts ($99) only Arduino's are supported. But this has the benefit of converting LabVIEW to native Arduino code that can run stand alone, unlike LINX where the Arduino has to always be tethered to a computer.