Many of us here (including myself) remember that old ugly launcher fondly. It was used for almost all of Minecraft's history, only recently being replaced by a shiny new launcher. Unfortunately an unexpected bug has arisen in the launcher's code, and since the old launcher is not able to be updated (unlike the new one) the bug cannot be fixed. Mojang has not gone into specifics about why the old launcher isn't working, but there is a good chance there will be more information from them in the near future.
Although many are suggesting Mojang may have shut down the old launcher, with even Nathan Adams saying "We put time and money into keeping it running longer even though it's been deprecated for over half a year", Mojang says the bug was not intentional. Nathan said on Twitter, "There's nothing we can do to fix it and so you'll have to update the new launcher." The bug is keeping all logins from working on the old launcher.
Unfortunately for those of you who cannot update to the new launcher for whatever reason, there is nothing Mojang can do. Users are being asked to update to the new launcher (if they can) or switch to a 3rd party launcher. Even worse, the bug seems to have affected most custom launchers as well. Rest in Peace old Minecraft launcher, we will miss you.
Source: Twitter