Is there a way to tell what might have happened to cause a major decrease in site traffic? Are there ways to tell what was the contribuing factor if a site has no outlinking to bad neighborhoods etc. and suffers a sudden 50% traffic drop? Also, how can a webmaster tell what link might be the contributor to a sudden burst in traffic? I have had high PR links show up that didn't have any effect on a site's traffic whatsoever. I've also had a situation where there was a sudden traffic jump and the traffic was not coming from any one source. How can we best analyze the cause of either situation?
Google Analytics have day-by-day stats, so if you see a major decrease on one day, you can just view Google Analytics for yesterday (or the whole week if you want to be accurate), see where the incoming traffic was coming from, and then view for the day where the decrease happened and compare the different sources of incoming traffic. Google Analytics also shows you incoming links from different sites, so that should help you with your second question. Google Analytics will tell you where your links come from. They split it into Search Engines, Direct Traffic, and Referring Sites.
Also check if your link partners are still showing your links or not. If your link partners drop you, then you will loose traffic...
You can track which of your links brings traffic to your site, and the over-all activity of your site by signing up on Google Analytics. Then as Quality-Content-Websites suggested, you have to check if your link partners removed your links that may have caused the sudden traffic loss.
Another reason is that your competitors are working harder on website optimization. In terms of links: It is not only important to have a good PR link but to have it from a relevant resource. read latest Google algorithm updates to learn a bit more on that
Along with Google Analytics, you can also use their Website Optimizer tool which allows you to try different variations of your site to see which combination is the most effective