Best headphones you've ever heard/used

I would definitely not recommend the EX71SL. I bought these headphones and I found them very muddied. The midrange is completely butchered. The bass is satisfying once you get a seal but the sound is just... horrible. What a waste of $50.
The etymotics are better, I havent heard shures, but they're supposed to be good. Basically you do compromise on any of these mini-phones, no doubt about it. Id pick the sub $200 HD-580 over the top of the line etymotics any day of the week. The Etymotics are still the best I've heard in a small package.
For at home listening, I would pick (in this order) the Sennheiser HD650, the HD600, the HD580 or the Grado SR-125 (havent heard any of the higher end grado's but I assume they'd be move up the quality range just like the sennheisers do.) I dont like any of the new Sennheisers as much (the 590s, etc.)
My opinion is stay away from Sony. At every price range above $40, someone makes a better set of headphones for the same cost.
Of course I haven't heard mega-buck 'phones like the Stax, so my choices are in the under-$500 category.
Also if your budget permits, buy a headphone amp. It opens up the music tremendously. Even the battery powered Airhead will greatly improve your iPod listening experience.

The problem with in-ear 'phone for me has always been the positioning or soundstaging. Even good in ears like the etymotics sound 'wrong' not because any part of the frequency range is off, but because the imaging is wrong. All headphones sound like the soundstage is inside your head to varying degrees, but larger open headphones are not as bad at this as any other kind. In ears dont even bounce the sound off your outer ear the pinnae (sorry if I spelt that wrong) and all the other ridges etc on your ear. Believe it or not this is an important part of sound shaping and decoding.
To me, the etymotics and I'm totally guessing here, the shures would have a similar problem. They get fatuiging fast because they your brain knows that the imaging is wrong. I can very well believe that not everyone has the same reaction to headphones and in-ears (and I'm still a headphone fan despite all I say) but that's my reaction to headphones.
Of course there are problems with open phones. Other pointed out the problems when using them outdoors. I listen to mine at night in the bedroom when I dont want to disturb, but I can still listen at reasonable levels. For other uses, other phones may be a better match.
Just my $0.02.

Head-Fi has great discussions from dedicated hi-end headphone folks who know and love their headphones. The issue with high end headphones is the requirement of a matching high end headphone amp, your existing amplifier / receiver can't do justice to high end 'phones. Of course it goes without saying a high end source is also a must.

The most loved phones probably are:
Sennheiser HD-650
Beyerdynamic DT880
Sony Qualia 10, R10, and CD3000 (in order of decreasing quality and cost)
Grado RS-1, HP-1
Stax Omega
AKG K1000
Sennheiser Orpheus

The last three are electrostats or other planar headphones, and usually need special amps. I personally have not heard the Stax Omegas and the Orpheus (rare and expensive).
Of the others I'd pick the Qualia or the Senn 650s driven by a high end headphone amp. The Qualias cost 6x more than the 650s though.
I haven't said much about the canalphones such as Ety ER-4P/S or the Ultimate Ears, etc. as I think they are only practical for use on planes etc where you really cant have your entire high end setup anyways, and I think they are very uncomfortable. They sound pretty good for small headphones, but give me any of the full sized cans I mentioned any day.

Oh, I missed the "wireless" requirement for the home setup. Well, there isnt a single high end pair of wireless headphones that holds a candle to what I just mentioned. The only chance I see is to use a wifi device, but then feed it to a regular headphone amp + headphone pair. So you would need a wifi enabled source player, a wifi enabled receiving device, an amp and 'phones. If you really care about sound quality, wireless is a killer.