headfi.org
Your wallet and family may never forgive you, but check out headfi.org (the premier headphone site). If you think people on the MacRumors forums are passionate/crazy, you are in for a surprise.
Having considered going overboard and, thankfully, pulling back, here are my favorites (all of which can be used without a headphone amp):
(1) Bose QC15 - You can read all you want about noise cancelling headphones, and hate Bose as much as you want as being a marketing driven company, but their noise cancellation headphones are great. I haven't tried their new in-ear NC headphones (QC20/20i), but the QC15s are excellent at noise cancelling. There is a reason just about every single serious industry review of noise cancelling headphones makes reference to these as the standard.
(2) PSB M4U 2 - This headphone has a built-in amp and noise cancellation (good, but not as good as the QC15s), and I think that they sound fantastic with the iPhone. They are big and heavy for a "travel" headphone, but the sound in a reasonable quiet environment, when you use just the built-in amp and not the NC circuitry, is tremendous.
(3) Sony MDR-1BT - I really love these as BT headphones. The sound is very good (not as good as the PSB's, however), and they work great with the iPhone, depending on the iOS. (Some iOS updates made these headphones work slightly less well than others, but never really an issue unless you are jumping around tracks all the time.) Not being tied by a cord, as silly as it may sound, it wonderful.
None of these are cheap headphones, but having spent a lot of time researching and listening, I really like these. If I could only have one, it likely would be the Bose because I use headphones most when I travel on a plane, and NC is critical. If I could only have one outside of travel, it would be the Sony, because these sound that good despite being BT.
There are many good headphones that are much cheaper, so shop around. I haven't written about IEMs because you are looking for on/over-ear headphones.
You can also go crazy, and it may be worth it for you. I listened to a pair of Bayerdynamic T5p's through a decent headphone amp. The detail, clarity and depth of the sound blow any of the above away, and that was still using an iPhone with 256K files as the source.
Have fun!