Sticker work: Small precise scissors (Fiskars brand). Brasso and cloth for removing prints. Brasso, Dremel, and polishing wheel for assembly-line massed shield de-printing. Prismacolor colored pencils for coloring the white edges on the final cut-out. Elmer's Washable GlueStick for attaching the prints.
Shaping/Cutting Plastic: Fine work, an X-Acto blade, usually the standard triangular #11. For heavier cutting, the thinner blade on my Victorinex (Swiss Army Knife). For really heavy cutting, Dremel and cutting wheel (I did the major cutting on the thick plastic of the beards with this, for example). You can break an X-Acto blade with potentially dangerous consequences if you force the blade too hard, so unless it is careful shaping, I tend to use the Swiss Army Knife (which has numerous useful attachments such as the pliers, awl, scissors, tweezers, etc.). I have a variety of small files for smoothing edges - but filing removes the shine and gives the plastic a matte look. I have 600 grit wet/dry sandpaper (fairly fine) but I haven't really used that on Lego stuff yet. Faster grinding can be done with a Dremel, but I find I can cut/slice and then refine quicker.
Clipping: I have been too lazy to get out either of my two nippers (one works along the side like a pliers, the other along the front like incisors and is useful for getting a flush cut) and have used my anvil clipper that is supposed to be for gardening. Clipping stresses the plastic and often leaves a whitened edge that has to be removed, so I usually clip short of the mark and then slice off any stressed-colored area.
For slicing apart 64x64 baseplates, I use a steel ruler and a heavy duty matte knife. Definitely do not use an X-Acto for this, and don't try and cut it all the way through in one pass (but then, I doubt many of you would want to do this).
Redwine the Ribald: Stare long enough into the abyss...
Two-Tonic Tippler: ...and you spit into it.