What is that blue gunk on my battery terminals?

The white or blue crusty gunk that develops around battery terminals is a reaction caused in part by fumes escaping from the battery reacting with the lead terminals and connectors. If left to its own devices long enough, it can eat the battery post, and also take the alligator clip on your battery charger with it.

You can clean this stuff off with a wire brush, after disconnecting the battery. To prevent this from happening, just coat the terminals and connectors with grease after reassembly. This keeps the fumes from getting into contact with the lead. Just throw whatever blue, green, or yellow grease you have handy on the terminals. You don't really need to worry much about conductivity through the grease, since the act of screwing down the terminals will squish enough grease out of the way that the metal will be in good enough contact anyhow.

Actually looking at your battery once in a while is a good idea, and if you have a maintenance-type battery, make sure it is properly vented, with the hose at the back right.