<p>We have one web application (sharepoint) that collects information from disparate sources. We would like to be able to link users to the main websites of those various sources and have them pre-authenticated. I.E. they enter their credentials for the other sources (which are a number of different types LDAP, AD and home grown!) and we retrieve some information for them, and remember there details (Possibly Single Sign-on to keep em nice and safe). The user can then click a link that will open the full app in another window already authenticated.</p>

<p>Is this even likely to be possible?</p>

You need to act as a web browser acts to different sites with storing credentials (usually in cookies) locally. Use therefore a  a proper client library with cookie support. This could go probably for most of sites. There are sites using HTTP authentication, which are also easier to access from appropriate client libraries.  The most demanding can be access to SSL websites, but again, most client HTTP libraries cover that nowadays as well.
All you need now is just to prepare your web application to act as a proxy to all those separate web resources. How exactly this is done in Sharepoint, well, I hope others will answer that...