Refused Connection?

Everytime i try to play a Minecraft Multiplayer server it says Refused to Connect then the server name. I recently Updated my Modem and wonder if that could be a problem. It usually takes me several tries before i can connect to even 1 server. When i Click the Multiplayer button on the Main screen. If i just sit there all the servers will have that blue internet bar keep moving or say Cant connect to server. How do i Fix this?