I've always wondered why there haven't been any efforts to generate artificial gravity via spinning spacecraft ala 2001.

Have there ever been any serious plans or proposals to do that?

Nautilus-X was pretty serious.

You really want a pretty large diameter so that you don't have a huge gravity gradient causing your astronauts discomfort. Tethers might be more practical than the classical doughnut designs for the near future.

JAXA recently brought up a small wheel into the ISS that can be used to simulate varying levels of spin on mice. Research into .4G gravity is particularly important if we're going to be sending people to Mars, but in general if lower levels of gravity keep mice and people happy those'll be easier to generate on future spacecraft.