It's day one with the new Bifrost and Asgard 2 setup, and I'm blown away.  These two have completely changed the way my PC audio sounds, and yet given me a path to even better equipment in the future.
 
Noise is non-existent, even in high gain mode.  Any noise I heard before on the same rig is now gone.  My headphones, a pair of V-Moda M100's, sound best on low gain, so that's where I'm leaving it.  This does not surprise me, as they have been capable of output on any 1/8th in. jack I've plugged them into.
 
You may have heard that these get hot.  They do, but not dangerously so, and not unreasonable for a class A amp.  My background in audio is mostly in home theater, and this is on par with one of the home theater class A amps in both sound and heat.  The knob also gets hot at the same time.  It is not untouchable, but you will notice if you're using it a lot.  I don't, personally.  I set it and forget it for most listening.  Further, since I'm using it as a computer DAC, I also have the option of OS volume control if it really bothers me.
 
Sound output on this amp is great.  If you want to deafen yourself, you can absolutely do that with this amp.  I don't recommend it, obviously.  The knob goes from 7 o'clock to 5 o'clock for zero to max.  I keep it around the 10 o'clock position and it's already well above theater reference with more than 180 degrees of knob to go.  Headroom, therefore, is ample. 
 
Sound is clean and uncolored from what I can tell.  They didn't do a great job of pointing it out, but this little headphone only amp has more capacitance than most home theater receivers by far, and more than some dedicated multi-channel amps.  Just when I think I'm getting used to the amount of clean bass output it has to offer, another song comes on that one-ups the previous ones and surprises me again.
 
At the risk of using buzz words too often, I now understand what people mean when they say ear fatigue.  I used to have that problem with these headphones, and I thought it was the headphones doing it.  Once I started using the Schiit combo, I've been able to listen for hours without my ears feeling tired, ringing, or experiencing tinnitus-like symptoms when I take the headphones off.
 
In summary, I cannot recommend this amp any higher.  I now have sound that competes with, and in some cases, surpasses, what I have accomplished in a dedicated room with home theater equipment and multiple subs, even while at work.  Amazing.  Grab it before Schiit realizes they can get way more money for this amazing little unit.

Amazing little DAC.  Fits easily on my desk without any hassle.  It even improved the sound of Pandora so much that I can barely hear the difference between their stream and local FLAC or uncompressed WAV files anymore.  Setup on Windows 7 was plug in and go.  Updated the drivers to the ones from Schiit's website just to get the additional sample rate options per their instructions.  Changing to the improved drivers was a breeze for anyone familiar with driver installations on Windows.
 
My only complaint, if I had one, is that it doesn't natively support DSD.  I don't actually have any DSD files to play, so that doesn't bother me, and the explanation from Schiit makes perfect sense to me as to why they didn't include it.  I do have some SACDs I wouldn't mind playing, but it's not really a high priority for me, as I use this primarily at work where I'm all digital.  If I really care about it in the future, I'll grab a DSD compatible player to plug into one of the toslink connections and switch input to that.

I purchased these headphones about 6 months ago.  The first thing I noticed was not the sound, it was the amount of pressure on my ears.  Within 15 minutes, my ears were sore from wearing them.  A quick look around found that many people had the same problem, and that the answer was to purchase the larger pads and replace the default set.  I did so, but still had issues with the amount of pressure that was now around my ears instead.  It took months to find out that the headband was meant to be bent little bits at a time to set the head size.  Stretching it out a couple times resolved most of the remaining comfort issues without making them loose.  As a result, I can no longer use the nice hard case they came with, because the case forms them back to the original size and shape every time I put them away.
 
On to the sound, these headphones can be driven by just about anything, but will definitely see a marked improvement using a good amp.  I have used them with standard on-board computer sound cards and cell phones and they sound better than your average headphone by far.  Connected to an Asus Xonar STX, they're noticeably improved.  I now have them connected to a Schiit Bifrost/Asgard 2 combo, and it's again a big improvement over the Xonar.  When idle, I would estimate they drown out 75-80% of the surrounding noise.  When playing, they drown out 99%+.  Bass is good with an ordinary amp, almost too hot with a good amp.  Running the "ultimate headphone test" at http://www.audiocheck.net/soundtests_headphones.php demonstrates a clearly audible 10Hz tone.  5Hz sine wave is nearly undetectable, but I suspect that is as much about human hearing as it is about product.  High frequency test, I hear tones starting at 18KHz (Update/edit: I found out after writing this that 18KHz is the highest I can hear, your mileage may vary).  Using the sweep tones, I do notice a couple of drops in volume both going into and leaving the "mid" extremities as it passes each crossover, but they are not large drops, and are well within the abilities of an equalizer to fix should one want to.
 
It is true that when driven hard and when a lot of bass is in the source material, the drivers can generate a little heat, but I have not experienced a scenario where the amount generated was uncomfortable.  Outbound sound leakage is almost non-existent.  If you put your ear up to the outside plate of them, you can hear it, but not without doing so.  Friends stopping in have repeatedly noted this to be true, that they can never tell if I'm actually listening to anything or not when they walk in if I don't tell them.
 
In summary, and with the caveats above that require some listener knowledge of the product to make them ideal, I would recommend these, especially to someone just starting out in headphone audio, as they make a very good stepping stone while you're still deciding on your equipment.

Very comfortable headphones for long sessions.  The microphone is a good sensitivity, and very uni-directional.  I don't ever have to do anything "special" for people to understand me.  I use default gain, and just put the mic near my mouth.  I also never get complaints about background noise. 
 
The stereo sound on these is good for gaming, and good for background music, but don't expect any critical listening.  Sounds are clear, if not a bit hollow and wide/distant, no matter the source material. 
 
I do not use the USB DAC that came with it.  It's quite frankly, junk, and in all cases so far, I've gotten better results using the on-board sound card on whatever machine I plug them into.  The added distortion and falsified surround, most of which appears to be gained using reverb, just isn't worth having the alternate sound card for output.  Positioning of the sounds is also only so-so when using the virtualized surround in most games.
 
Plugging them into a nicer DAC/AMP brings them to life.  I cannot stress this point enough.  These headphones are severely limited by the sound card you plug them into.  Plugging them into the on-board jacks sounded good.  Plugging them into a Xonar Essence STX (with its dedicated power connector for amp and op amps) sounded noticeably better, especially where bass impact is concerned.
 
Isolation on them is good, but background noise is still possible in a noisy room.  Nothing that turning them up a little bit won't fix.  Volume is more than sufficient for just about any environment using a basic sound card.
 
Over all, I'm very happy with these and would recommend them to most people looking for good gaming audio.