When you say ‘over the ear’, supra-arural, ‘behind the ear’ with hooks or plain ordinary headphones? The only thing I can gather is that I couldn’t imagine you’d mean earbuds.
With normal headphones, they’re a small bit out of your budget, with the lowest prices on google products being $35 before tax and shipping but I personally really like the Sony MDR-NC40s for the first category. They’re very comfortable low pressure headphones with very delicate leather and really rather brighten-up the music allowing you to hear some better amount of detail when you have the noise canceling function on, which requires one AAA battery to operate. They can operate without the noise canceling function but they kinda sound rather much like your plain ordinary $10 or $15 set. I noticed a few years after I bought them that they were given a best selling headphones award at my local radio shack.
As for cons, some do people complain that the balance is off and I don’t trust that I have a very good frame of reference to confirm or deny this. I must also admit that these aren’t the sturdiest headphones on the planet. I have two broken sets where the earpiece just came off with relatively low amounts of force with only about one year of use out of each.
As for supra-aural, I often hear they’re quite uncomfortably tight but the Sony MDR-V6 headphones can be had for about shipping included and I always hear good things about the original’s sound quality wherever I read about them. They’re a professional monitor series Sony’s been making since at least the eighties. Again they’re out of your price range but $43 (including flat rate shipping) isn’t that bad a price to pay for top quality sound and they should be much much sturdier than the NC60s. I think I’m going to order a set right now, in fact… One other issue that should be pointed out is that after about ten to twenty years, the ear pads will wear out but Sony’s still making replacements thus-so-far.
I have another set of broken radioshack brand headphones that were rather large with thick padding that I got from Radioshack for exactly $25, after what I believe was 50% discount on clearance. The sticker on them says 04A02 and that’s all I know about them. Memory’s too fuzzy to recall what they really sounded like but at the time I thought they were decent. Granted, up until that point I’d never spent very much on headphones. That was so long ago that you probably can’t find 'em anymore though anyway.
Within your budget these logitechs sound decently clear for their price, if they’re the same ones as what I’ve gotten from the office supply store. Certainly look like the same item. However I dislike the way the holders bend your ears and without them, the posture you need to keep them on is quite a (literal) pain in the neck.
I have no experience with sennheiser whatsoever but I do hear they make a good product. Usually the products I hear about are much more expensive than $20 dollars though. I don’t think they’re very well known for their ‘budget’ cans and are primarily notable for being more of a high end company.
Perhaps it’s all this is not exactly what you’re looking for but hopefully this is useful information in some way though.