If you are designing / programming a website then it is particularly important that you check that it works correctly on several different browsers and different versions of that browser. Browsers are updated fairly often but if people do not have automatic updates turned on then they may not realise that the version they are using has since been update one or twice at least. The first time someone may realise their browser is out of date is when they start to notice several websites are not displaying correctly. Sometimes this is the issue for the user but if your browser is not out of date or only one version previous then this may be an issue with how the site has been programmed This can be extremely frustrating and often causes people to leave a site and go elsewhere. Often this problem is caused by browser compatibility issues where the website has not been programmed correctly to work on multiple platforms. This is often an easy fix but it may go unnoticed for some time, during which you could be losing customers.
There are websites that allow you to type in the URL of your site and it will check the compatibility for you. There are so many previous versions of browsers that it is virtually impossible to get a site to look identical on all but you should try and ensure it works for at least the last two versions.