Masking Tape

Masking tape works on eggs, too.  The edges will be a little fuzzier than electrical tape, but it depends on what look you are going for (and, often what you happen to have around the house).  This example is pretty tame, but you can cut out letters, shapes, and more.  I once did a landscape image on an egg with different "layers" of mountains and such.  You have to really think backwards - but it works!

Electrical Tape Eggs

Using electrical tape is one of my faves - you cut it into pieces/shapes/letters and adhere it well to the dry egg (use the back of your thumbnail to rub). Drop your egg in the dye, remove tape, dye again if you like... and you are good to go.  You can get really intricate and spell out words, make pictures, etc -- with sharp, crisp edges.  

You can even save the pieces of tape and reuse them a few times.

This is electrical tape.  It's NOT the same as duct/Duck tape.