I've driven mine very successfully with 1) Schiit Modi3/Magni3+ stack, 2) Schiit HEL DAC/Amp, and 3) iFi nano iDSD Black Label portable DAC/Amp. All three rigs have slight differences but all sound great. I was most concerned with the iFi driving the 300 ohm HD6XX but I'm running the volume about 1:00 at good listening level so no problem - impressive little device.
I have a Schiit Asgard3/4490 on the way as well...
A lot of folks really seem to like an OTL tube amp for these phones though. I can definitely see a Bottlehead Crack or something similar in my future.
I drove my HD600's with a Modi/Vali combo and was very happy with that setup. If you want to try a solid state amp that is budget priced but has a lot of juice, the Topping A50 is a nice little amp, very powerful and transparent.
Back when I bought the 6XX I was using an iFi Zen and I have to say it was a fantastic pairing. You'll definitely want to use the 4.4 Pentaconn output though if you want some good volume. The bass boost function on it was awesome with those cans also. Not a bad setup for around $350 (all-in) or so.