There’s always something that either consumes or is consumed by the thing your are upgrading. Given the example of browsers, IE7 to IE 8 is a big jump. Thankfully MS put the compatibility mode feature into IE8. There are a lot of web apps that fall apart because they were specifically written for the old way IE did things. I would suggest you compile a list of sites that your users use everyday. Be sure to focus on any internal sites. Upgrade some test machines and do some compatibility testing.
It never fails, someone releases an new version of something to something and shortly there after someone figures out how to exploit it. Keep up on the products you upgrade and learn how to keep your infrastructure secure if this does happen.
There are always a few that slip by. Again test test test.
Testing and research is the key.