whats with the...?

[Rudeboy]

I've been flipping around ebay (bad habit, i know) at some older basses and i've noticed a lot of classics have some little plastic pieces attached to the body.

They're usually plastic diagonal strips, one on either side on the strings above the bridge.....

well, there are some on this bass:
http://cgi.ebay.com/Vintage-1960s-Su...QQcmdZViewItem

i was just curious as to whether they surved a purpose, what they're called, etc...

[Beavinator]

If I'm not mistaken, you're looking at the thumb rests. For example, I usually place my thumb on the neck pickup of my jazz bass. But, this bass doesn't have the neck pickup, so instead you'd rest your thumb on that plastic piece...

[PaleMelanesian]

I agree. On older Fenders, the rest was below the strings. This was for resting your fingers while your thumb plucked the strings. They eventually realized that nobody played that way and put it up on top as a thumb rest.