Today I was driving around town and started to smell something kinda like burnt plastic, and then my spedo stopped working. It fell down like it does when the key is off. I took out the dash piece and looked and there was nothing burnt or blackened. I checked all the fuses and they're all good. I was wondering if I could get some help on this.

does your odometer and cruise control still function normally?

Vehicle Speed Sensor(VSS). But there should not be any "Burning Smell" associated with the VSS malfuction. Still, I would look there.

My Grand Prix has been known to do that as well.
My tach, and speedo will just die
I am fortunate enough to have a scanner to verify that the VSS is still working, I have traced the problem to a bad voltage regulator in the cluster.
Long story short, GM wants $400 for a reman'ed cluster, so I learn to deal with it.

By that I mean everything except the burning plastic smell.

If you smelt burnt, I would think it was something inside the cluster itself that took a crap. I mean it could be as simple as a resistor or some other component that may not look burnt but is.