Web browsers are an essential tool for a desktop computer. Various browsers are available, and the default one on your system is not necessarily the best choice.
On a Windows system, the default will probably be Internet Explorer (IE). Because of this fact, this browser is currently the most popular browser in the world (around 85% of the market at the end of 2005) but the market share has been steadily going down as of 2009. This may be because of the issues discussed on the malware page, it is not the best choice. The most standards compliant version is IE 8.
Firefox is the most popular alternative browser. It is fast, free (both gratuit and libre), has an excellent user interface, is full of nice features and is much less susceptible to malware than IE. It is also extensible and skinnable. It is available at http://www.getfirefox.com One useful feature is that it is the most cross platform browser.
Opera is also excellent browser. It is fast, free (in the sense of gratuit), has an excellent user interface, is full of nice features and is much less susceptible to malware than IE. It is available at http://www.opera.com and has been made available for a number of other operating systems.
Safari is also a free excellent browser. See Apple Macintosh for more details. It is available at http://www.apple.com/downloads/ .
Chrome is also a free excellent browser which presently has extensibility issues but is fast and minimalistic so has an excellent user interface. It is available at http://www.google.com/chrome and almost certainly will become cross platform.
The down-side of using the alternatives to IE is that some webpages are written to take account of the oddities of internet explorer, rather than being standards-compliant. This means that sometimes, webpages do not display properly in any of the standards-compliant browsers, but this is a shrinking problem. Also, you can always use IE for these particular pages, as there is no limit to the number of different browsers you can have on your computer.
The commonest browsers on the Apple Mac system are Safari (from Apple), Firefox and to some legacy extentInternet Explorer (from Microsoft). IE on the Mac may not suffer from as many problems as it does on Windows, but it is still problematic. In any case, Microsoft has now withdrawn all support for IE on the Mac, and new Mac users will find other browsers that are somewhat better.
The main options for Mac users are Safari, Firefox, and Opera.
Safari is a very good browser (the rendering engine is based on Konqueror's KHTML engine), but some users have found that it incorrectly displays pages more often than Opera or Firefox.
The list of web browsers available for Linux users is, of course, huge.
The most popular graphical ones are probably Firefox and KDE's Konqueror, although Opera is also available.
Terminal-based browsers include links, lynx and w3m.
This will always be an issue with any browser as they are extremely complex pieces of software with multiple possible routes of exploit via open exposure to the nasty world. Some browsers are quicker at correcting reported issues than others. You should always run the latest release and never assume that that will keep you totally safe as zero day exploitation is possible and you may have installed extensions with bugs or allowed behaviour yourself that is not the default most secure option. Some browsers have extensions that are strongly recommended such as Noscript for Firefox which can make some popular forms of exploitation of browser's much more difficult.
These can bypass all the security features of your browser. Extensions can do so to a lesser extent. Microsoft observed correctly that the Chrome plug in for Internet Explorer that actually creates a web compliant browser out of IE increases your security risk as you effectively have two browsers to keep up to date. More importantly an almost universal add-in like Adobes Flash (or Reader) creates a zero day exploit issue for the user. Firefox has started prompting when plug-ins are out of date as few plug-ins do this themselves. However equally important for plug-ins such as Flash that are now nearly universal is that the default settings are unacceptable in the master browser. Ensure for Flash that you go to the Flash Settings Manager to configure Flash on any computer you should use and want to keep reasonably secure and private.
There is competition but all have to have a similar basic browser feel.
There is immense competition. Functionality is now generally emphasized over features for the core browser following the success of Firefox which removed legacy Netware feature bloat.
There has been a general drift towards more standard compliance. As of 2009 the only major standard not being definitely worked towards in the major browsers is scalable vector graphics (SVG) and this is because IE has not made the commitment. It is notable that a plugin for IE that supported SVG had its development stopped for almost certainly commercial reasons and some think other commercial reasons are behind this lack of commitment.