As part of website optimisation, support for all the major browsers (and versions) is incredibly important. For example, Internet Explorer prior to version 10 is lacking in support for some major features, such as animations (which you’ll see if you compare this site between IE9 and say, Google Chrome).
Where the issue arises, is supporting a feature for modern browsers, can actually break a site altogether on an older browser. It’s therefore necessary to create fallbacks for these browsers by specifically targeting them. When you have multiple browsers and versions, this is no small task, but none the less it’s something that I undertake with every project I take on.
Legacy browsers are also supported with some features to ensure that the still functions on a basic level to get your message across, although with a browser such as Internet Explorer 8 (which has been abandoned by Microsoft) there will be integrated messages to inform a user to upgrade their browser, with a link as to how they should do it. A user won’t be left in the dark as to why their site isn’t working, and they’ll be educated on the reasons for moving over to a browser that supports modern styles and functionality.