Woofer pumping - what gives?

Could it also be low frequency feedback from the speakers to the turntable ? If your turntable is not well isolated from the speakers you'll get this problem (I did a few years back). If your speakers are spiked into a wooden floor (either directly or through a stand) and if your turntable is on a rack or piece of furniture that is also sat on the same wooden floor then I bet you've got feedback.
I solved it two ways : either wall mount the turntable, or place the turntable on an isolation platform. I made my own isolation platform from a concrete slab and a thick wedge of foam. In either case the "wobbling woofers" were completely cured.
The above answers are also good reasons for your situation, but if your setup fits my description then try a simple isolation platform to see if it makes a difference.

If your turntable has a dustcover, I'd suggest removing it–that could exacerbate low-frequency "feedback" from your speakers.

Do the woofers "wobble" when playing stuff that has no low bass? If so its not feedback. Im guessing Sktn77a has got it right.

blkadr ... my woofers used to wobble even when the record was just cued up and the track hadn't started. I think that subsonic feedback can occur just due to warping of records. For the wobbling to be visible as wobbling (and not a blur) the frequency will be well below normally audible frequencies. so I'm not sure the amount of bass on the track in question is relevant.
That's not saying that my diagnosis is correct, just that you don't have to be playing a bassy recording in order to notice it.

Seandtaylor- Did this occur with all records?