I think Kenny nailed it pretty well. There was a certain purity to Knotts' comedic style that rendered his characters hilarious regardless of script, setting, or premise. The fact that The Andy Griffith Show and Three's Company were such drastically different sitcoms illustrates this point. Knotts fit seamlessly into both worlds.
Don Knotts fun fact: Originally, the Barney Fife character was envisioned as a straight man, with Andy Taylor being the main comedic force (Andy Griffith had a substantial career in comedy before The Andy Griffith Show, as anyone who has had the good fortune to listen to What It Is, Is Andy Griffith can attest to). You can see this in the show's pilot episode.
In other news, I'm going to be working seven days a week for the foreseeable future, so I won't be blogging very much. And God knows when I'll pick up my drawin' pen again.