>>Why are they so desperate for links that they're offering money
C'mon, not everyone that wants to buy a link is desperate, not everyone is looking for a PR benefit. Has everyone forgotten in this Google microcosm that the web is also about presence?
I have clients that look for links on sites that get high traffic and all they are looking for is a piece of that traffic. Before Googlemonster came along people weren't overly concerned with links from other sites even being on topic. Links were about traffic.
If I write a bit of anchor text that makes people want to click on it where do you think the best place for that link would be? On some on-topic site that gets 500 visitors a week or on a site that gets 30,000 vistors a week?
>>How do I figure out how much to charge?
Charge what the market will bear, and what your conscience allows. If the price seems high to you then lower it.
There are some considerations, if you are worried about diluting your site's theme then the links should be to sites with similar content or scripted. If you think they are trying to buy Pagerank and you don't like that idea ask them if they mind if you script their links. If they only want traffic they won't care, if they are after PR they will definitely care.