I think John is right, this has nothing to do with your RAM. More RAM might make the circle disappear faster
What kind of circle is it btw? Is it a beach ball
Image
or is it a spinning wheel?
Image
I'm just gonna guess it's the second picture (spinning wheel).
If you really want it gone, you should reinstall Lion and make sure you don't install software that takes a while to shut down.
When I shut down my mac, I always have to wait ages for transmission and playstation 3 media server to close down.