I somehow tapped somewhere by mistake, and a list appeared with all the IP numbers and dates of my recent logins. Where can I find that again? It seems interesting.
There's nowhere on the site itself that you can find this information. It is logged internally, but not exposed.
However, if you use Stack Exchange's own OpenID provider to log in (which you do), you can view your login history there: https://openid.stackexchange.com/user
If you use a different authentication provider (such as Google or Facebook), you'll have to turn to them to find your login history and associated IPs (I know Google provides this information in some fashion; not sure about anyone else).