The "beats" brand are really expensive, so if you're looking for $50 and under, don't worry about those. Plus they are not worth the cost, so it's a double "do not buy" recommendation
The AKG K518 or Harman Kardon K81 DJ models (which I believe are just rebranded but the same headphones) can be had for under $50 on sale if you keep an eye out. They fold up so they can be stashed away easily and are nicely portable. Haven't heard those exact models, but my AKGs are my favorite headphones that I've heard
Sennheiser also has a variety of small portables that are pretty good, the HD 2xx line - 228, 229, 220, 219, etc. I've tried a couple of those and they sound nice for the price, and are comfy and small. There are a whole range of prices and styles, some of them are in the sub-$50 price range. (I don't recommend the PX portables, I had those and didn't like them at all.)
I see a lot of people wearing Sony MDR series headphones, they have a good reputation also. Some of them seem like they'd fit the bill, and Sony is well-known, but I have no experience with their headphones and I'm not sure which models are supposed to be the better ones...
ETA: If you like research, check out joker's thread on portable headphones on head-fi. »www.head-fi.org/t/433318/shootou ··· 12-02-12