Assuming new Linux users are coming from Microsoft Windows, they'll all be at least familiar with MS Internet Explorer. But asside from IE, there are several popular browsers available for Windows that are also available for Linux.
Firefox is a very popular opensource browser for Linux, Windows, and Mac. This is my browser of choice. Very active development, fantastic features, and the countless extensions available make this a great browser for both internet novices and power users. Many distributions (including SUSE) have custom packages of this browser available within days of official releases.
Opera is another popular multi-platform web browser with an eye on standards-compliance. Opera is not opensource, but it is free (as in beer). Until recently, the only free version of this browser was ad-supported, paying customers could remove the ads; but now it is free for everyone and no ads. Opera is widely considered to be the fastest of the full-featured web browsers, and this has been my experience. It is also known for its seemingly-endless potential for customization. Opera is my second-favorite web-browser after Firefox. Opera has also taken the commendable path of offering their software in many popular formats such as RPM and DEB for various Linux distributions and even multiple versions of the distros. I really admire Opera for their innovations, decision to release their browser for free (beer), and their fantastic support of Linux; this is a company offering proprietary software that Linux fans can get behind.
Konqueror is KDE's default web browser. Like MS IE, it also doubles as file browser (I love Konqueror as a file browser, but rarely use it as a web browser). Because it is part of the KDE project, it is tightly integrated with the rest of a KDE user's desktop. It is a very capable and feature-rich web browser.
Epiphany is the standard GNOME web browser. I have personally not spent much time with this browser, but if you like other GNOME applications, you'll want to at least give this one a try.
Popular CLI (text-only) web browsers: Lynx, Links, w3m