Your browser is your portal to the internet and it is an emotive subject for some the choice of which to use. Some applications work better with some browsers than other browsers then there are some legacy applications that only work with old versions of Internet Explorer. In my professional opinion and my experience you should use something new and keep it updated.
On my computer at work I keep the following browsers installed
Note If you are running Windows XP or older I would strongly recommend you to install Chrome or Firefox and update Explorer to the latest that you can. Earlier versions of Explorer are buggy and exploitable by criminals. Please note all browsers have weaknesses and exploits are found regularly in all of them but old versions of Internet Explorer are the biggest target.
Then there are positive reasons to change browser
The auto updater works well and in the background keeping your install of chrome up to date without the hastle. Mos the other others are following suit and implimenting their own updates.
Google services integrate well into Chrome indcluding the excellent bookmarks sync and the tab sync between devices. See this page for more info.
Hidden hint – For an advanced look at a page composition hold down the ctl shift and I keys then reload a page for some really cool info.
Well known and mature. Firefox has been about for over a decade and has come along way. The length of time that firefox has been about means that it has had the most exposure to web developers other than Internet Explorer. The add ons for firefox are a huge asset and I know many web developers who swear by Firebug add on.