This is one part that really drives people crazy. IE-specific ActiveX controls, as opposed to plugins that work in almost all browsers (such as Flash or QuickTime), force people to use IE to load a given page (or a whole site) whether they want to or not.
Sadly, this usually isn't a design move that you can just undo, since it's often rooted in other technology decisions. Consider Netflix's Watch Now function, which lets you watch movies streamed from Netflix's online library in a browser. The required plug-in is IE-only, because it uses a security wrapper and codec provided by Windows Media Player. There's no way to change something like that without reworking the entire content delivery mechanism.
A. Move away from ActiveX entirely. Again, this isn't always something you can declare by fiat -- especially if the decision to use or not use ActiveX isn't something that is in your hands. If you have the clout to do so, suggest as many non-platform-specific alternatives as you can. Solutions written in Flash are probably the best substitute for ActiveX multimedia controls, and there are a great many third-party Flash controls to choose from that offer such things.
B. Compel non-IE users to use ActiveX compatibility controls. This seems like an interim solution at best. It is possible for Firefox users to run ActiveX controls using a Firefox plug-in, but a given user might not be in a position to install said control, and even if they are, they may not want to do that.
This is a relatively minor issue, but one that became significant for me when I tried to write an Ajax-based chat application that used it. It's possible to bind hotkeys (Alt + a given letter key) to certain Web controls, like form buttons, by using the accesskey attribute for the control in question.
The problem is that the browser isn't always obliged to implement the chosen access key, especially if it overrides an existing browser command. The way the hotkey is invoked also varies from browser to browser -- and even varies among iterations of a given browser. In Firefox 1.x, the default was Alt + hotkey; in FF 2.x, it's now Shift + Alt + hotkey. It's possible to reset the default behavior with an about:config hack -- change ui.key.contentaccess to 4 -- but I've found people aren't always willing to make changes like that for the sake of a couple of sites.