As of September 19th, you may find that Minecraft will no longer connect to our server due to a protocol bump in version v1.6.4. Bukkit currently only supports the protocol version used by v1.6.2 which provides you with only one option: Downgrade.
Downgrading with the new launcher is fairly easy, but it may be non-obvious:
First, you'll need to create a new profile. By doing so, you can easily switch between the latest version and the previous version that our server is running at. To do so, click the "new profile" button:
Next, configure the profile. I usually select a profile name that reflects the version I'm downgrading to such as 1.6.2 in this particular example. Be sure to select the correct version as well (release 1.6.2) and then click "save profile":
Easy!
Also, I apologize for the ugly appearance of the dialog boxes. Mojang doesn't have the launcher use a GTK/KDE look and feel for the Java Swing library, so it defaults to the standard "metallic" or "metal" theme (I can't remember the name, I just remember that it looks like a horrible throw back to the 1990s).