Those are called earphones or in-ears.
The Ultimate Ears SuperFi 5/vi are great because they come with foam tips. Basically any earphones that can be fitted with foam tips will be best for you.
I suggest you take a look at
http://complyfoam.com and see what earphones are supported so you can choose accordingly. You should know that these foam tips are expensive and need replacing after a month of everyday use.
Shure SE115 also have great in-ears that come with their own foam tips that you can take a look at.
There are just so many good choices out there, but you need to be a little more specific on your spending limit and sound preference.