It has been a problem for many players now, 8th and 9th april with people having trouble connecting to their servers. This is a result of the new 1.7.6/1.7.7 update. It is actually a minor update to help introducing the new UUID system, but it is not compatible with older servers. I am now going to tell you what the problem is, and how to solve it. Skip down for how to solve it, thats probably what you need.

The problem
When mojang implemented the UUID changes in the new 1.7.7, they had to change the servers too because the servers had to change from usernames to UUIDs for storing player data. All your server need is a little update. If you are the server owner, this is the link you are looking for.
https://s3.amazonaws.com/Minecraft.Download/versions/1.7.7/minecraft_server.1.7.7.jar

How do I, as a client, solve this?
You can do it as easy as downgrade your minecraft to 1.7.5.

1. Open your launcher
2. Select "edit profile"
3. Select "release 1.7.5" from the only dropdown menu
4 Select "Save profile"
5 Press play and enjoy your servers!

EDIT: Most big servers got an update that solves this problem, but many are still running on the old version, included my own.