Please note that the Minecraft multiplayer session servers are online and are not experiencing any issues at this time. http://help.mojang.com
Upon the release of Minecraft 1.7.2, the netcode for multiplayer was changed quite a bit. As a result of this, when viewing your server list or attempting to connect to a server, you may see "Can't connect to server", "Pinging...", "Can't reach server", and other similar errors. If the server you're viewing on the server list or trying to connect to gives you one of these errors, it hasn't been updated to 1.7.2 yet. Unfortunately, Minecraft will no longer display the "outdated client!" error upon you trying to connect or when looking at the server list, which is very misleading to most people. The only way to fix this problem is for the server owner(s) to update the server to Minecraft 1.7.2 or for the user (you) to downgrade your client to 1.6.4 or earlier.
This post has been updated as of January 2nd, 2014. Please ignore anything that is crossed out. Anything that is crossed out is outdated information.
If you are using CraftBukkit, you cannot update your server to 1.7.2 yet due to the fact that the Bukkit team has not released a new development build for 1.7.2. You can expect to see one within the next 2-3 days.
CraftBukkit for Minecraft 1.7.2 was released on December 1st, 2013. Two beta builds followed. Please note that these builds are not guaranteed to be completely stable. As a precautionary measure, you should always backup your server files before updating. Additionally, your plugins may break upon updating. Please keep this in mind and make sure to update your plugins immediately after updating. Failing to do this can result in severe instability of your server.
You can download the latest CraftBukkit builds for 1.7.2 here.
If you are using SpigotMC, a new development build (completely unsupported, only availiable due to high demand by the community) is availiable for download and use on your server. From my testing, this build is pretty stable, although as always, certain plugins may break upon updating. You can download Spigot for Minecraft 1.7.2 here. If you don't know what Spigot is, please see this page.
SpigotMC has also been updated to Minecraft 1.7.2 (What is Spigot?). Just like Bukkit, you should be very careful when updating to new builds. Always make a back up of your files and upon updating, update all your plugins (if they have any new versions availiable) immediately. Failing to do so can result in severe instability.
You can download the last SpigotMC builds for 1.7.2 here.
If you are a user and have updated to 1.7.2, but none of your servers have updated, you can connect to them once again by opening up the Minecraft launcher, clicking "edit profile", "use version" > release 1.6.4 After logging in, you should be able to connect to any server that is using version 1.6.4.