The Palomar Knot is arguably the strongest all-around knot. Due to its use of a double line, it is as efficient at maintaining a high breaking strength as it is easy to tie. Furthermore, it is versatile and can be used for monofilament, fluorocarbon, and braided lines alike.
To tie a Palomar Knot, take the tag end of the line and double it back a generous length. Thread the entire double line through the eye of the hook, then make an overhand knot with the double line. The hook is then threaded through the original loop at the end, and the entire knot pulled taut to complete the Palomar Knot.
The Palomar Knot can also be used for specific rigs such as the drop shot rig, which requires a hook some length above the terminal end of a leader, to which a small sinker is attached and used in finesse fishing situations. To ensure that the hook stands out perpendicularly from the line, tie a Palomar knot with an extra long tag end, and thread the tag end back through the loop and use the end to attach the sinker. This rig can also be used as a general trailer-style rig, in which a smaller lure is attached to the middle hook with a larger swimbait style lure at the end, mimicking a fish chasing a small bait.
Here are the knot strength efficiency numbers for the Palomar Knot as tested across the three major line types.
See the Fishing Knot Strength Chart for more data and details on the testing methodology.