Hardly there is the best browser. There is a group of the most advanced or adequate.
Also, "the best browser" may depend on the OS:
Windows has several most used: Internet Explorer, Firefox, Google Chrome, Opera, Safari. Other most adequate ones has one of their rendering engines or several. I.e. they are in a way re-packing of the same. Although these browsers do have their certain advantages over the major browsers. SeaMonkey, K-Meleon, Maxthon, etc.
Mac OS X is dominated by Safari. But other major web browsers have Mac OS X versions too.
Linux, FreeBSD, OpenBSD, Net BSD, etc situation is similar to the one of Windows except there is no Internet Explorer and Google Chrome exists mostly in its specific forms like Chromium or Iron.
There are also less widespread OS like Haiku or AmigaOS of some kind and more.
Mobile devices are quite diverse, so you have to specify which is the one you are interested in.