I'm relatively young, so my internet experience started with good old Netscape, which still exists to this day as a heavily morphed and altered version of itself - Firefox. Internet Explorer was Microsoft's answer to Netscape's success and the growing popularity of the internet.
However, the browser wasn't written from scratch; in true Microsoft fashion, the company licensed the codebase for Spyglass' Mosaic, and built Internet Explorer from that. The funny part is that in some way, Internet Explorer and Netscape (and thus, Firefox) are relatively close relatives; Marc Andreessen, who founded Netscape, was a Mosaic developer.
Rivalry ensued, leading to rapid development paces on both the IE and Netscape ends; back then, Microsoft wasn't a follower when it came to web browsers - they were setting standards, too. IE 3.0 was the first to include support for CSS, and IE5 introduced XMLHttpRequest, the basis for Ajax. In the meantime, Netscape blessed the web with things like the blink and marquee tags. Remember that around this time, Microsoft released Comic Sans, so let's call it karmatically even.
For the release of Internet Explorer 4.0, Microsoft had created a giant 3 metre high version of the "e" logo, which was dropped off in front of Netscape's headquarters overnight with a sign that read "From the IE team ... We Love You". Netscape tipped the logo over, and and placed a giant version of its dinosaur logo on top of it, with a sign that read "Netscape 72, Microsoft 18" - in reference to the market share figures of the time.
The laughing would soon stop over at Netscape. Microsoft's Internet Explorer became the better browser, and was distributed for free from the get-go. On top of that, it became part of Windows itself, which pretty much stopped people from downloading anything else. IE became the dominant browser, with at one point a market share of 96%.
Without any competition to speak of, development came to a halt, and it would take Firefox - it used to be called Phoenix - rising from Netscape's ashes to kick IE's butt into shape. Microsoft is getting there - and the browser wars have returned.
And we, customers, benefit from it all.