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, available in the konqueror package, is KDE's web browser (but can also assume the role of a file manager). 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. KDE also has a newer browser called Falkon, available in the falkon package. It uses the QtWebEngine.
Users not satisfied by any of the above can use Firefox. This browser, available in the firefox-esr 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 package). This browser is developed by Google and has become the most popular browser in just a few years. 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™.