For the brands mentioned, I broadly agree with them this time round in my limited experience, but I can't really judge more broadly than a few brands there and as others have mentioned, they notably miss any Beyerdynamic offerings.
It really depends what you want. I have a pair of the Koss KSC-75 for my portable use and they're fantastic. They cost about $50 and are clip-over-the-ear sort of things but have some of the best sound below $100.
For home use, I use a good ol' pair of the Alessandro MS-1 (which are essentially the Grado SR80i, albeit with some slight differences that make them more preferable to most). They're also an open headphone but are fantastic and come in at about $125-$150. They excel more at the rock end of the spectrum and aren't heavy on bass, so if you like thumping dance music then maybe avoid them but that's not to say the bass isn't there. They're a good, balanced offering for all types of music listening.
Note that both of the above are open headphones, so they will not block external noise. Depending on your use case (e.g.: isolation for coding) this may be a major downfall. Open headphones are invariably better audio quality for the equivalent price however, so you're hard pressed to get a good set of cheap closed headphones.
I'm happy to recommend both, depending on what you want to do with them. Alternatively, there's a fantastic website run by some knowledgable people who can give you some input even if you don't end up ordering from them, at www.headphones.com.au . Obviously an AU retail store, but their forum is good for discussion and they have a mostly-sensible set of recommendations.
So much of the online head-fi like chatter on this subject is near voodoo. I bought some Alessandro MS-1's which are tweaked Grado's after delving deep into online opinions, and they're peaky inferiors, an opinion objectively shown by an obscure online debunking I later found.
Beware popular opinion. Grado SR-80i's are good value for money, detailed but they have flaws.
Shure SRH 440 (around $60) or 840 if you can afford them ($150); they're over-ear (closed) which beats active noise cancellation in most environments, they have a rich, deep sound, they're sturdy... and Sure came out first in this survey! ;-)
It's really more helpful if you give a budget, but I think you'll find very few people who wouldn't recommend the ATH-M50. From what I've owned, nothing hits the price:performance ratio as sweetly, and it is great-sounding no matter what genre I throw at it.
They are closed-back, so the soundscape is limited, but still great. I wear them on planes and they passively cancel noise well.
I have the Sennheiser HD 280 pro, which I love. They are comfortable over-the-ear, flat frequency response, a little bit of attenuation (just enough to cut down background noise so that the music covers it, and decent on a plane, too), and really comfortable. I can wear them all day with no problem (no problems with my glasses, either). One of the best $100 that I've spent.
I find The Wirecutter to be very trustworthy for all gadgets. Top notch research across the board. For headphones they even have a "Which Headphones Should I Get" section if you aren't sure where to begin.
Find an old pair of Sennheiser HD-580s. They were so good they un-discontinued them. Been using the same pair since 1999, with the same cable they came with (apparently the cable can be problematic.)
home: Grado SR-80 (great sound, durable except for the cable; also, the cable is in Y configuration and twists a bit. I had to replace it after a couple years).
If I had to buy just one of these, DTX 501p win hands down as the most versatile.
What exactly broke in yours? I've had mine for 5 years and except for the cable (had to replace it) and the pads (foam) they're holding great. And I can't say I look after them much.
First plastic decal with model name in the middle of the earpiece came off in a month. OK, not a big deal - I can use them without it. But then, after few months of use, side plastic holder slipped off from the headband, which is metal. I plugged it back, but overtime it became too loose and doesn't hold anymore (obviously plastic latch inside the piece is worn off).
I like retro look, but cheap-looking plastic shouldn't be actually cheap, you know.