You cannot really really hide, not totally! Online status can't be hidden 100%. Other residents can still see when you are online if they are in the same group and they can use scripts to tell if anybody on the grid is online.
Map hiding does not work as much as it used to. If another resident is in the same sim or near your sim, she can see your name on the mini map in SL 1.23.
Busy mode is dangerous. If you try to buy stuff from Xstreet or a scripted vendor you will pay your money and not receive the item. It does not even go to your trash, it vanishes!
Access lines only work for 50 meters over the ground. Ban lines only work for 768 meters over the ground. Other avatars can still see you with camera controls.
You only get real real privacy if you use a secret avatar and hide on a closed island.