Huh. The Leave It to Beaver theme song had a name, and it wasn't "The Leave It to Beaver Theme song." Wikipedia tells me that it's called "The Toy Parade," by David Kahn, Melvyn Leonard, and Mort Greene. I don't know anything else by them, and the ad at the top of Wikipedia that I assume is begging me for money is making me feel guilty for researching this month.
The weird thing is that I couldn't figure out what song was running through my head for the past few days. I had to hum it to someone at work, and then lost several points from my geek-cred. I'm losing it, I tells ya.