When I try to log into Minecraft it connects online and my skin is there in single player but when I try to go onto a server it says bad login (If I try to login on Minecraft.net it lets me)
The Mojang Minecraft servers are down or having instability issues right now. It affects everyone.
For private servers owners can (temporary) set online-mode to false in the server properties file. That will then skip the check, but it will also open up for trouble: Hacked clients and users can login under other users names.