There are several web browsers available in Debian, including the version of Firefox known as Firefox-ESR.
As of 9th of June, 2016 the package Firefox-ESR replaces Iceweasel, and is in Wheezy and Jessie security repositories.
In Debian earlier than Stretch, the iceweasel package is a transitional package for Firefox-ESR as described above. To install it run:
# apt-get install iceweasel
Chromium (The open source web browser behind Google Chrome)
conkeror (keyboard focused web browser with Emacs look and feel based on Firefox xulrunner engine)
firefox-esr (Extended support release of Firefox with Debian patches)
Iceweasel (Firefox ESR rebranded for Debian)
TorBrowser (Modified Firefox ESR. Protects privacy.)
Default Web Browser
Once you have more than one of them installed, you can select the default one system-wide using:
update-alternatives --config x-www-browser
update-alternatives --config www-browser