In general, don't ever allow it to install. No website should need it and thanks to the way Internet Explorer is built if you allow an ActiveX component to install via your browser it doesn't adhere to the security zones set by you.
While there may be a few web apps on the Internet that may require you to install ActiveX components they are massively outweighed by the number of spyware/malware/trojans that use this method to deliver their own special brand of "joy".
Interestingly Firefox, while having an extension that allows you to install some ActiveX components, doesn't have it as default and strangely I've never had problems with surfing..