Taking price into account above all else, these are the best headphones I have ever owned.  Obviously my HD650s and DT880s sound better, but they also cost 15-25x as much. I've probably put ~150 hours on them. I did do the kramer mod (involves drilling a few holes in the driver cover to allow more sound through) but they sound great even without the mod. I also bought a Parts-Express headphone from Amazon, took the garbage drivers off them and snapped the Koss drivers on. I find them much more comfortable this way. As a plus you can bend the headband however you like to suit your comfort level. Some people do the "quarter mod" where you put a quarter over the earpads (after taking them off the drivers) and cut out a circle to allow more sound through as well. I chose not to do this because I love their sound with the kramer and headband mod.
 
I listen mainly to electronic music, so people who listen to more jazz or rock might not like these as much as I do. But for trance, dance, dubstep, these are simply amazing. My DT880s show me new things in my music that I've never heard before. It's one of the things I love most about them. Now this isn't me blowing smoke... but there have been times I heard something on the Koss that I've never heard before. This includes faint vocal tracks in the background, synths, and little things here and there.
 
These are my work headphones, because they allow me to hear people talking and not completely isolate me from my environment. Some people say they leak too much sound to use in public, but I use them in my cube and no one has ever complained about hearing my music. I don't crank them up but I certainly don't listen quietly. I use them straight from my phone (Nexus 4) and they sound great. I brought my Fiio E17 to work once to try them amped and I just felt like they lost some of their magic. Don't ask me why, or how, I don't know. All I know is that they didn't have as much sparkle, which is something I love about them.
 
I'm no expert in describing audio, but I'll do my best. They have a great attack and decay on the notes, which to me translates to good PRaT (pace, rhythm and timing). The space between notes is very discernible and they just get me groovin'! The imaging is fantastic as well. I can clearly hear music going from side to side, and even in front of and behind me to a degree. The bass is punchy and extended. It also has a great texture to it. It's not muddy or bloated at all. They're also very airy and have a nice open sound to them. The treble is sparkly but unfatiguing (in my opinion). Some people find them a bit too treble-forward, but I have experienced almost no sibilance from them. Mids and vocals are good, nothing amazing but they're not recessed. Female vocals are quite nice on them, with male vocals almost as good.
 
I honestly think these are worth $75. I might be slightly more critical of them at that price, but these are so cheap, I have literally nothing to complain about. I don't plan on recabling them because I love them just the way they are. I bought 3 pairs over the holidays to give to friends. I only ended up giving away 1 pair. These are just... so good. I'm more satisfied with these than I am with my HD650s.
 
What Koss has done here is simply magical. I would never have dreamed something so good would be so cheap. I honestly could not love these more. They are my favorite headphones out of all that I have ever owned.
 
Thank you, Koss. THANK YOU!!!

I'm just gonna start off by saying I love this headphone. It has dominated my head time since I got it. My HD650 gets no love anymore. They are just incredible. They're easily worth $400 in my opinion.
 
My first serious headphone buy (HD280 5 years ago not included), I got the 250ohm version and used it with an E17 for a month; I ended up returning them to Amazon due to getting the HD600 and HE-400, both of which I ended up selling and returning as well. I couldn't justify 2 pairs, let alone 3. I got the HD650 and it changed everything. I ended up selling/returning everything. Once I got the Lyr and Bifrost, it changed everything. So that leads us to early December 2012...
 
I had the money and decided to get myself a little sumpin sumpin if you know what I mean. I got offered a sweet deal on some great condition 880/600s and leaped at it. And here I sit, writing this ridiculous rave review about them.
 
What I love so much about them versus the HD650, which is great, is that they're exciting. The treble is sparkly and clear. There is a nice air to the music, something spacey to it. It's awesome. The HD650 is a bit more closed in and intimate. I listen to a lot of electronic music, so I expected to like the DT880s more. What I didn't know is how much more I would like them. Now, maybe I'm exaggerating... but they're the spice that my music needs! They make everything lively. With a little EQing, the bass is thumpier and wobblier. The best part is that the Lyr has an insane amount of head room, so they never clip or distort. It's just cerebral.
 
Versus the DT880/250s on the E17, the mids are much better and bass goes even lower. With the Lyr there's even more detail to the treble as well. I see now why almost everyone has the 600ohm model. It's just better in every way.
 
I can wear these for hours and my ears might get a little warm but only due to sitting inside earcups for 2 hours! They're light, sturdy and have just the right amount of clamp. In contrast, I think the HD650 is a bit tighter.
 
I think they're worth just as much as HD650s, because if you amp them right, they will reward you.
 
Source: MBP (optical)
DAC: Schiit Bifrost
Amp: Schiit Lyr
Tubes: 1972 Orange Amperex PQ (Holland)
 
Compared to the stock GE tubes with the Lyr, the DT880s are more revealing but warmer. Bass might be the tiniest bit less? But mids are even better. They sound almost just as good as my HD650.
 
Oh, and they work plugged into my iPad 4 @ ~80% volume. Perfect for movies and music. It's nothing special but it works!
 
-- TL;DR --
 
Basically to sum it up, the DT880/600s are some of the best headphones I've heard in my life, if not just due to my preferences. But their combination of detail retrieval, airy soundstage, incredible positioning, balanced but satisfying bass, and unfatiguing, sparkly treble is just...something to behold. It works well for almost everything, provided you have high quality source material.
 
Best value at this price point, in my opinion. Other close competitor is the HD600, which is great too, but emphasizes different things.
 
I love my DT880.