Sounds like the bearings going out. While the bearing themselves are cheap the labor to replace them is usually high. Many opt to replace at that point unless your super handy.

I'm with Larisa...

Either the bearings are going or the spider is starting to break down causing wobbling of the drum rubbing against the outer tub and boot.

Twelve years is a good run now a days for any washer.

They don't build them to last long anymore.

I would definitely look for a new washer.

I appreciate the feedback, folks. I can wobble the drum back and forth considerably, which sounds like another tell tale sign of a spider or bearing failure. It sounds like it's time to go shopping.

yes, most likely bearing failure. Soon you will see water leaking from underneath. The seals go, then the bearings get wet and start to rust.

There was a video on line some time ago done by someone who replaced his bearings and spyder. It explains why it costs so much, being at least 4 hours of labor and a near complete disassembly of the machine in order to reach the bearings.