Almost any tool might be used to construct mobile sculpture, however, there are a few tools that I utilize more than others. They are:

Needle nose pliers - Used to bend, shape, and twist wire.
Wire cutters - Used to cut wire.
Tin snips/Cutters - Used to cut various materials (metal, plastic, etc.).
Brazing torch - Used to work metal, connect pieces, and heat-treat materials.
Small anvil - Used to work and form metals.
Hammers, wrenches, clamps, vise, files, etc. - Used to... you know.

The most important tools I use, though, are my knowledge of balance, color, and style... all wrapped in my childlike playfulness and sense of wonder.