As promised we'll go a bit deeper in the styles of headphones.
Disclaimer: There are some types of HPs to which I'm not particularly fond of, so my experience with them is not as wide as with other styles, but they share certain characteristics that can be easily compared and for this entry I'll stick to 3 of them: comfort, sound & general applications.
This kind of headphone is extremely popular because they are cheap, small, portable, lightweight and if designed and used correctly almost non-intrusive.
When you evaluate the comfort on this little headphones you usually find that some brands are very well designed while others are a pain in the ear... When you design something that will be mass produced, you need to consider ergonomics and designers and engineers "play it safe" using the average size of everything, that way short, tall and average people can use the product. In the case of Earbuds this is a very important factor because you'll be using your external ear to position the headphone, specifically you put it inside the "concha" supported by the tragus, antitragus and anthelix.
Every ear is different from another, just compare your left and right ear and you'll notice small variations on size, angle and depth between them. So when you position the earbud it can fit like a glove or never stay in place. If they are well designed with no sharp edges and enough weight they'll work like a charm, some of them include some foam tips/covers or rugged plastic around them for better grip.
Talking about sound on this kind of headphones don't expect kicking bass and subwoofer like extension, simply because they leave a space between the driver and the ear canal, the environmental sound easily leaks "killing" low frequencies. They have a mid centered sound so the human voice is very noticeable or forward from the other sounds. The higher frequencies are also well rendered but with a limited range, you usually notice a gap between the mids and the highs, like if you can only hear the central mid frequencies and the high frequencies, the feeling like if you miss some sound information.
This kind of headphones are for the casual listener that demands portability over sound quality.
I don't recommend them for commuting or plane usage, they'll let all the noise in and you'll need to pump the volume to not very healthy levels.
You'll get a pair of this in almost any cellphone that can play music, you can get them for free in the bus or airplane; and you can find them in almost any convenience store.
There are hundreds maybe thousands models in the market so its very hard to give some advise on what to buy but the sure bet is to look for a serious brand like: Sennheiser, Sony, JVC, Pioneer, Philips, etc.