Is there a simple mysql command that can tell me how active our database is?
mytop; it's a bit of a pain in the butt to use, but seems to work well enough for the simple stuff like this.
$ mysqladmin status
That'll do for one-off measurements. If you want a more long-term view of mysql's load, I'd recommend checking out Munin. Out of the box, it comes configured with a mysql queries per second graph.