User Agent Switcher will do that. I notice there is a negative comment about this extension on the Mozilla extensions site. You may prefer to
go here instead. Extensions at this site tend to be updated more quickly.
You'll have to give FF permission to download from the site (gives a warning bar at the top of the browser). I have installed all extensions for FF from there for some time now with no problems resulting.
The extension can be left operational all the time, although perhaps that isn't a good thing to do. Site writers won't be inclined to do anything about their IE only sites if other browsers always identify as IE. I generally e-mail webmasters these days and say the site won't work properly in my preferred browser. I've had some positive answers too.
Answers such as, 'Why don't you take your browser and...!
Well. not really

Most say they will do something about it in future updates.
Opera has the option to identify as IE as well.