I've had this happen a number of times and it always temporarily gets me gummed up so I thought I would describe this problem and resolution here because I'm sure others have seen it too.
Assume you have configured a SharePoint web app to use SAML claims, and the IP-STS is ADFS 2.0. What I see sometimes is that after SharePoint redirects to the ADFS login page, the browser just "stops". The status says "complete", like it's all done and that's all there is too it. The address bar in the browser shows the correct ADFS server Url. So no error shows up, the browser looks like it's at the ADFS login page, but you are never authenticated, never prompted for credentials, and never get back to your SharePoint site.
In that case the problem I've found is that I have a proxy server configured in your browser, and the request is being redirected to the fully qualified domain name of the ADFS server (i.e. https://adfs.foo.com). In that case, you need to go into the browser (by the way, I'm describing this for IE users, not sure what the process is for other browsers), into Tools…Options…Connections…LAN Settings…Advanced. There is an edit box there for exceptions, which is basically a list of Urls that the proxy server will not try to resolve for you. If you add the Url for your ADFS server to that list then save your changes, you should be able to successfully redirect and get authenticated.
Unfortunately there is zero feedback from the browser in this scenario as to what it is actually having a problem with. So if you get the "Blank Screen of Death", consider this tip.