I'm going to agree with the couple posters who said that many commonly designated mid-fi phones can, indeed, present the sound quality of hi-fi, but it's really about the entire system and not just the headphone. I also think some phones that are pretty well known as hi-fi cans can sound very mid-fi, or just plain horrible if paired poorly (thinking O2, K1000 right off the bat).
At the same time, there are a couple headphones that clearly stand out when compared against all others, even when the others are in optimal rigs, and even when one's taste prefers another (i.e., I can acknowledge how really amazing and "superior" the HP2 or O10 is, yet not prefer its sound to a HD650). Compare a good HE90 rig to a killer HD650 rig. Compare a good R10 rig to the best CD3000 rig or even a D7000 or D5000 rig (markl's ears excused). Etc. I'm betting that to over 90% of listeners, with any background in audio (key piece), the specialness of the former will be evident. That doesn't kick the other headphones into mid-fi status. Pairing the 650s will a portable amp, for example, will kick it into mid-fi status with the flick of a switch, but that goes back to the point grawk and others have made.
This topic has come up many times, and it somehow always eventually falls into an argument about specific headphones, with someone feeling his favorite should qualify; then others get in tizzies about the high price of some models, and claim that ego and money determine what hi-fi is, and it's all b.s.; and then objective vs. subjective arguments start with folks on both sides blasting away at each other and all sounding like fools; and then the folks who love to argue the hardest, but often have the least experience with the full range of headphones available in multiple rigs, kick it up to some flaming personal attacks; and then someone finally comes in to say it's about the music, which it would be except that this is a gear forum; and then someone jumps in to claim any headphone talked about on head-fi is hi-fi since the rest of the world is listening to ibuds; and then, at last, after pages and pages of same, it somehow it all settles back to the same collective-wisdom list of headphones that has been around for years with an addition now and again, and that list starts the next thread months down the line so it can start all over again. Whew. Are we there yet?
My take:
Before people go around deciding they know which headphones are hi-fi or mid-fi or low-fi or whatever, they need to have heard a pretty full range of headphones and have also heard them in different rigs, preferably for more than five minutes in a noisy room, but even that's better than nothing. Let's take the K701/2 for example, and it's even better if you don't care for the sound signature. If you're coming from the unamped stock headphones with your dap or even a likable $50 pair of closed headphones picked up at Best Buy, and then compare that to the K701s running out of a computer with lossless files, a good external dac and a Heed CanAmp (well-match system, imo), I'll bet most folks with that background will say the K701 qualifies as hi-fi, even if they prefer a different sound. Then let's take a recabled, balanced K701 and pair it with Tyll's Krell source and a HeadRoom Max or a TTVJ 307A. Now let's hear what folks think hi-fi is vs. mid-fi vs. low-fi is. Bose headphones are hi-fi to much of the population, and that's just with people who have access to Bose headphones. When you're on an audio forum, the definitions and scales of meaning change, and the general gab that goes on here should accept those differences in meaning and respect the context (of being on a audio gear forum), and not want to argue or dummy down that point, even if there are differences in opinion about what qualifies.
There is a difference between being able to listen critically and listening for enjoyment. One is a learned skill, and takes time and concentrated effort; the other, thank goodness, is a basic gift to humankind. Back in the 80s, when I first got exposed to headphones and critical listening, I lived with a well-respected music producer. I was often in the studio when things were recorded. During the mixing and mastering process, both in the studio and at home (this was back in the day of R2R), he used both speakers and headphones obsessively to work things out. He'd sometimes ask my opinion about "this bass line" or if I thought "that whatever" sounded right or true or somesuch something. I couldn't even hear what the heck he was talking about, let alone form an opinion, but over time, with a lot of attention and concentration, nuances and subtleties I couldn't hear at all before, became quite clear and shockingly obvious. Some folks I know have critical listening skills far more honed than mine, and when they say, "but listen to this," I'll have to really pay attention in a way I often don't enjoy. Sometimes I can hear what they're talking about and sometimes not. Etc. and on. The point I'm obviously having a hard time getting to is that what often differentiates hi-fi from mid-fi exists in the very nuances and subtleties many people just don't hear, but are clear as day to others, and that should be taken into consideration when folks talk about this stuff on a forum dedicated to audio gear. Enjoying music is separate (thank goodness) and very personal, but is not the same thing at all.
There are a few headphones that are simply a notch-above the rest. It really doesn't matter if folks want to argue that's it's subjective or objective. If you don't agree with a general consensus formed over many years on headphones like R10, HE90, Omegas, L3000, HP2 after spending time with them, that's fine (liking them is a different matter), but you'd be part of a tiny minority, though I've seen that be a point of pride for some who regularly like to buck the tide around here. Go for it if you choose, but it usually says more about you than the gear.
People need to just get over the money thing. Most hi-fi gear costs more than other gear, if not the headphones, then the components needed to bring them from mid-fi to hi-fi. Yes, the price of some high-end gear is crazy stupid, but it is what it is, and doesn't change the sound quality one iota. Sure, there are always exceptions to be found. Yes, if you DIY, you can sometimes create a hi-fi rig for mid-fi prices, but a beta22 still costs more than a Starving Student, and an HE-90 with an Aristeaus will still smoke a D5000 with a 6-channel beta (nice rig I heard once).
There are a few headphones that scale exceptional well, and the fact that the differences and improvements can be noted already tells us that we can find lines between mid-fi and hi-fi even with the same headphone. It also doesn't matter if you have the world's best headphones, you can always make them sound like ass if you pair them with components that cripple their capabilities.
Well, I had a couple more points, but I'm really tired of typing, which means you're probably tired of reading, and I want to go out into a rather nice day here in Florida. The cat has decided he doesn't like his food and I must obey, I need to wash my car, I have a pedicure scheduled for 5:00, and then it's out dinner with friends. It's easy to get stuck in our little world, but it's much better to put it all in perspective on most days. I'm going to head outside to listen to my really crappy low-fi radio in my car so I can sing off-key and be very happy.
Happy listening, folks.