I've been contacted by an overseas research company having a client with an interest in using (parts) of a nine minute web video I did a couple years ago on the subject of gambling addiction. They have offered to pay a licensing fee to use the video within their client's project. How much should I charge- or, at least, how should I think about this? Is there a standard (or standard paperwork available on-line)?
Everything is worth exactly what the buyer will pay for it. In my opinion there is no formula here, I think it all comes down to how valuable the media is to them, and how good of a negotiator you are.
Questions that might affect the price - what's the nature / quality of the content? What they will be using it for? Are they asking for exclusive rights? Will they be using it in a commercial capacity, i.e. making a profit from the work itself? Would the content be difficult or impossible for them to acquire through other means, i.e. producing it themselves?
If you feel that the media is of high value to them, and that they have a good financial incentive to buy your work rather than self-produce or obtain similar work elsewhere, then you can and should hold the upper hand in negotiations. Otherwise, take what you can get and be happy to have made money from an old endeavor!
Also, just to be sure, did you produce this video on your own, or was it done for a client? May sound obvious, but if this was a work-for-hire you can't really license it out to others.
It's hard to say without knowing more about what they want it for. In addition to Brendan's suggestions, it might be worth finding out how they want it - if they're after a high quality master that would indicate that they're in a higher level game (and therefore you could charge a lot more) than if they just want to use the web clip.