Epiphany, the web browser in the GNOME suite, uses the WebKit display engine developed by Apple for its Safari browser. The relevant package is epiphany-browser.
Konqueror, the KDE file manager, also behaves as a web browser. It uses the KDE-specific KHTML rendering engine; KHTML is an excellent engine, as witnessed by the fact that Apple's WebKit is based on KHTML. Konqueror is available in the
konqueror package.
Users not satisfied by either of the above can use Iceweasel. This browser, available in the
iceweasel package, uses the Mozilla project's Gecko renderer, with a thin and extensible interface on top.
Last but not least, Debian also contains the Chromium web browser (available in the chromium-browser package). This browser is developed by Google at such a fast pace that maintaining a single version of it across the whole lifespan of Debian Jessie is unlikely to be possible. Its clear purpose is to make web services more attractive, both by optimizing the browser for performance and by increasing the user's security. The free code that powers Chromium is also used by its proprietary version called Google Chrome.