I already own a few headphones, namely the Audio-Technica ATH-Pro500MK2, ATH-T500, Sennheiser PX 100 II & PX 200 II, and the Philips Downtown and Uptown (Rule #3). I’m thinking of adding a new one and I can’t decide between the Beats Solo 2, Grado SR80e, and Sony MDR-10RC (budget constraints). I listen mostly Pop/Rock and Classical music and I have a cheap (Fiio E06) headphone amplifier.
That depends on what you’re using them for and how much you’re willing to spend. At the high-end, over-ear and in-ear headphones can both perform fantastically. For those of us not willing to spend thousands on headphones, over-ear headphones typically offer better bass response and a bigger soundstage, but in-ear headphones are significantly more portable and convenient — especially wireless earbuds.
Earbuds have small speakers that rest on the ear canal of the wearer. These are usually much less expensive than on-ear and over-ear headphones and reproduce the sound well. However, outside sounds, such as traffic or power tools, can get past the earbuds and interfere with your enjoyment. Earbuds also don't stay in place very well if the wearer is moving much, such as exercising. These also are lower fidelity than on-ear and over-ear headphones.