Plastic gloves to protect from electro-static discharge?

No, they do the opposite and build up static on the outside of the glove and from rubbing on your hands. Not a good idea if you like your electronics.

They also often have powders on them that you don't want to get on electronics.

Now there are specialized static gloves that work wonderfully and I highly recommend. BUT, these are not your run of the mill gloves. They are special ones.

EDIT: There has been some confusion with proper procedures relating to static, So I'm throwing it in here too.

Proper Static Guidelines

To follow good static safety procedures, you want to make sure there is no difference between YOU (the person), the equipment your working on, and ground (literally, the actual ground.)

The way that we do this is to use a number of possible pieces of equipment and procedures. First we usually use some piece of equipment to keep ourselves from having a potential difference in electrical current from the ground. An example of this would be the Anti-static wrist band. Now the wrist band comes in multiple flavors: ranging from a screwed down version that will ground itself to the table (and from there to the wall plug and from there to the electrical company's ground either outside the building or back at one of their power lines) or through a strap that plugs in to a wall outlet (skipping the table portion of the previous example) or has an alligator clip that allows you to clip onto the station that you are standing at without removing your strap.

All of those versions of the wrist band do one thing: keep you and the ground at the same electrical potential. Now the problem here arise that, even if you and the ground are the same level, what if you and what you're going to be working on aren't? Then there is still potential. This is why you want to ground yourself to the case or a ground screw or something like that in the device you're working on. That way you (who are already at ground potential) have just brought the whole devices ground potential down to nothing. This way it is safe for you to touch the components on the devices without worry that you will have a difference in charge from the device that will find the path of least resistance through the random chip that you touch and push waay to much voltage through it, frying the chip. You also want to repeat grounding the case to you and the ground every few minutes to make sure that nothing has built up in the mean time from you moving around.

Now, responding to a point made by another answer-er, you do not either want to overly handle the devices PCB overly much. These are covered in enamel in most places, yes, but they are also very sensitive to the oils in your skin. And these oils will wear through the enamel and cause problems over time. The best way to avoid this is to handle the PCB either by the edges, or by the case (which just grounds you to it all over again :) )

Should you have to touch the PCB directly, it is recommended to clean the board with a astringent like pure rubbing alcohol to clean any oils off and then dry the area with a clean cotton swap or ball or lint free rag.

There you have it: Psychodata's Guide to static electricity, electronics, and the ground. Now go not fry electronics!!!