I love my Sennheiser HD600.
They’re about $300 USD on Amazon, and they deliver some of the most natural and beautiful sound I’ve heard, especially because they are open-back.
They may not have the sound profile everyone is looking for, but to me they sound the most “real”—nothing is over or under emphasized artificially.
They won’t provide much rumble if you love lots of bass, but if you equalize them a tad in the lower ranges, you can somewhat fix that.
You will definitely need an amplifier and a DAC for them, though. The FiiO E10k pairs well with it, especially with the built-in bass boost function.
Depends on use and cost you're looking for, but for music Grado headphones sound truly amazing. For $125 the SR-80x are pretty wonderful: https://www.whathifi.com/reviews/grado-sr80x
This is the type of headphones experience that forces us to listen to whole albums during our testing, and before we know it we’re emotionally engrossed...
Greatest pair I ever owned were the Beyerdynamic DT 1770s. Closed back headphones with the greatest soundscape ever. The proprietary, piece of shit removable cable is enough to ruin them for some people though.
Koss Porta Pro. They're wired over-the-ear headphones. I've used both just the headphones, and the ones with a mic in them.
Things I like about them:
They hit a wonderful spot between sound quality and price. I can never talk myself into the really expensive audiophile headphones, but I can talk myself into these and they are heads and shoulders over the other headphones I've tried in the same price range.
Over the ear but not sound-isolating works for me b/c I wear glasses and game and the really big and bulky over-the-ear tends to press the arms of my glasses into my head to give me headaches. The Koss Porta Pro don't stop outside sound, but I have to be wearing Koss Porta Pros over 12 hours to get any sort of headache, whereas with the over-the-ear sound-isolating ones headaches can happen in 20 minutes.
I don't like earbuds because the bass is shit in the price range I like, and they're easy to lose, and most importantly, I have small ear canals and have never found an earbud that actually stayed put in my ear.
Things I don't like about them:
The wires are so thin that long-term I tend to break them at the plug or at the place where they part to go to each ear, or in one case, I severed the wire by accident by rolling over it in my chair. And my wire repair skills are not great.
They're made to fold up for easier carrying around I guess, and I don't actually use that feature. But because they do fold up, they can catch hair on your head and rip it out painfully.