Used to check if an account is premium or not. Returns true if the username is a premium Minecraft account, returns false otherwise.
http://session.minecraft.net/game/getversion.jsp?user=<USERNAME>&password=<PASSWORD>&version=13 OR http://login.minecraft.net/?user=<USERNAME>&password=<PASSWORD>&version=13 OR https://login.minecraft.net/?user=<USERNAME>&password=<PASSWORD>&version=13
The Minecraft launcher uses this to authenticate logins. If the username and password are valid for a premium account, returns "<POSIX time>:<hash of password???>:<username with correct capitalization>:<freshly generated session id>:". If username and password are invalid, returns "Bad login". If the username and password are correct, but the account isn't premium, returns "User not premium". If the given version number is less than 12, returns "Old version". The username is not case-sensitive, but naturally, the password is.
It is also possible to cause an error that breaks this page. See Breaking getversion.jsp for more info.
This link is keeping your session alive.
http://session.minecraft.net/game/joinserver.jsp?user=<USERNAME>&sessionId=<SESSION ID>&serverId=<SERVER ID>
This link seems to be called when a server with online-mode=true checks if it should allow a player to join the game. The session ID is generated by the launcher when you log in (you can also generate them with the "getversion.jsp" link above). The server ID is the server's identity. This URL will return "OK" if the given session ID is the last one to have been generated for that username; otherwise it will return "Bad login".
This link is check you in the server or not. The server ID is the server's identity. This URL will return "YES" if you are login the <SERVER ID>. otherwise it will return "NO".
http://s3.amazonaws.com/MinecraftSkins/<USERNAME>.png OR http://skins.minecraft.net/MinecraftSkins/<USERNAME>.png
Returns the skin for a given username. Case-sensitive, returns an XML access denied page if the skin doesn't exist.
I think this is used to create the classic server list. I have no idea how all the parameters work (which is why I didn't change them from what I found on the Google page), though some of them you could figure out. Returns a link to a classic server page (have not investigated the effects of the params on the link fully)
A test page that Mojang asked people to use as they worked on a new launcher for Minecraft. Runs a few processes in the bwoser, then starts a new version of the launcher, which will be downloaded to /.minecraft/launcher as launcher.jar (only known difference between this launcher and the normal one - this launcher has the new logo)
This link gives a glimpse at a future feature to Minecraft. This page says that, in the future, it will be possible to have Minecraft open and connect to the server IP specified in the URL when you access this link. See it for yourself!
Apparently some sort of joke page. It says it is triangulating a satellite and sending benchmark data back to Mojang or whatever, but a look at the source shows it is just an animation.