COMMON:
Bad Login usually will happen if you are running Tekkit/Another Minecraft Launcher and Minecraft at the same time, having two accounts running at once will not let one of them connect. To fix it you can log off of one of the launchers, or if you only have one launcher open you can quit minecraft and wait a few minutes (~3) then restart it.
Another common reason is because you may have not purchased Minecraft at all. When you do not own a premium (Purchased) Minecraft account but play anyways it will only let you play single player and if you try to connect to a multiplayer server it will not let you connect unless the server is cracked which 90% of servers are not cracked, to fix this just buy minecraft. Another fix is try deleting your Minecraft Bin folder or update your minecraft, you could be getting the error for an outdated client. When you play minecraft in Offline mode, it will not let you connect to multiplayer servers because of that (Similar to not purchasing Minecraft problem).
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UN-COMMON:
Your Java may have outdated, you can find many places online to see if your Java has been outdated or if it is up to date. Another uncommon problem is you have a consistently bad internet connection and it will not let you join the servers, you can either get a better internet company, move the router, or just move where you go on the computer closer to your main internet location. The most uncommon problem is when you cannot connect but all of the problems above were not the case. This could be because your firewall is stopping Minecraft from working, there are many ways to get your minecraft working through the firewall.
I hope you liked my little encyclopedia!
If you have a network issue, please post here to help the server owner find problems/solutions:
viewtopic.php?f=3&t=37897
