In my work, I commonly use an internal SharePoint web site that is exposed to the internet. This site uses Windows Integrated authentication, which is really handy, as it means I generally don't need to type my user name and password repeatedly, which is great!
When I switched to Vista, I noticed that I always had to type my username and password--I'm guessing that this has to do with the fact that I access the SharePoint site using its external URL, so IE can't tell that it's really an internal site. (I had also had to do some configuration on Windows XP to get that working correctly.) One way to solve this is to add the site to the list of IE trusted sites, and tell IE to automatically send your user name and password. In case you're having the same issue, here are the steps to configure a trusted site to automatically authenticate.
First, navigate to the site you wish to trust. Next, open the Internet Options dialog in Internet Explorer (click Tools, then click Internet Options.)
Click Security to display the security tab, and then click the Trusted sites zone:
Next click the Sites button to display the Trusted sites dialog:
(Note that you had to navigate to the site you want to trust first.) Click Add to add the site, and make sure that the checkbox to require server verification is checked. Click Close.
At this point, you've added the trusted site, but it will likely still require you to enter your credentials on each visit. To change this, click the Custom level... button on the Security tab to configure the security settings for the trusted sites zone:

Now scroll down to the bottom of the settings list, and change the setting for User Authentication to Automatic login with current user name and password:

Now click OK, and then OK to save the settings.
Interestingly, when I tried this, I had one issue--I could not navigate to my trusted site reliably. Often the browser would seem to get stuck while downloading the content, and IE would just "sit and spin". (Occasionally it seemed to work okay--it was just really slow in those cases.) Someone suggested that I try deleting my browsing history (I used the Delete all... option) and that worked! For some reason, having old cached data confused IE--not quite sure why, but it works fine now!
In a partially related note, the IE 7 authentication dialog in Vista can be a bit tricky:
There's a Remember my password checkbox in the dialog, but it doesn't appear to do anything. If you check it and then enter your user name and password, the next time you visit the site, it will just ask again. This is Paul Thurrott's favorite IE inconsistency (search for "remember my" on the linked page.) According to Paul, Microsoft says that this is by design. Perhaps that's true, but if so, I really don't understand why they left the checkbox there--it seems like some sort of strange UI decoy.