The first two things that came to mind:
1) Ren and Stimpy - Log ("It's Log, Log, it's better than bad, it's good!")
2) Twin Peaks - The Log Lady
Log from Blammo!
Scene with the Log Lady and Major Garland Briggs from "Twin Peaks"
I can't believe "Ren and Stimpy" and "Twin Peaks" are over 20 years old!