Tie a knot in a thin piece of wire, such as a highly flexible jewelry wire, by hand. If the wire is springy, you might have to put two or three knots in the same place on the wire to keep the knot from coming undone. However, the more inflexible the wire, the more likely it is to snap. Carefully plan exactly where you want your knot, so you only have to do it once. Knotting and unknotting a less springy wire may create a weak point.
Tie a knot in difficult-to-bend wire with a pair of jewelry pliers or needle nose pliers. Short pieces of wire that are hard to get a firm grip on with fingers will also respond better to knotting with pliers. You may use pliers on anything from jewelry wire to bicycle spokes. Before you begin forming the wire into a knot, decide the points at which you want to hold the wire with the pliers, because the pliers may leave a slight rough spot behind. When pulling the knot tight, go slowly to ensure that the knot closes where you want it to.
For extremely thick or hard-to-handle wire, a table vice may be necessary for holding one end of the wire. To avoid marking the wire, use a vice insert with a circular hole for holding the wire. If the wire is long enough and flexible enough, you may be able to use your hands to make the knot and your body weight to pull it tight. However, if the wire is stiff or short, try using pliers or vice grips.
You don't always have to make a knot in wire. Use a small metal crimp on the end of a wire to keep it from fraying. Pound the end of the wire flat with a hammer for a decorative end-cap that will retain beadwork. You can also use a soldering iron to fuse two or more wires together. Or, if the knot is intended to be decorative, try using a different decorative element -- a spiral or a zig-zag, for instance -- that can be easily formed with a pair of pliers.