There are probably a couple hundred "browsers", though most of these use the Internet Explorer core and only provide an alternate shell.

"Unique" refers to including a rendering engine as opposed to using one already included on the system. It does not discriminate against browsers that use the same or similar rendering engine but integrate it directly into the program (such as Chrome and Safari).

Internet Explorer*

Mozilla Firefox

Apple Safari

Opera

Google Chrome / Chromium*

Seamonkey

K-Meleon*

Dillo

Arora

Netscape

Grail

W3m

Slipknot*

*currently available only for Windows

Maxthon

Avant

WebbIE

AOL Explorer

UltraBrowser

iRider

MSN Explorer

Sleipnir

Enigma

NetCaptor

Runescape "stand-alone" client

GreenBrowser

Lunascape

Runecats Explorer

Teega

Tencent Traveler

Yahoo Browser