Well, Scyess, I have to agree that a problem with doing a Garfield-esque regular strip (in my case, probably more Penny-Arcade-esque) is that even after a mere 65 comics, already there's more than one strip that's really only funny because of the established background: I like to think the "Cock And Goat" motif in my comic is funny, but if it's the first thing you see then it has no meaning at all.
I like the fact that you, as you say, do a more definite series (and include character bios in your personal info type bit to make strips easier to understand) but also have clearly marked random doodles. If I have a really, really good idea for a non-continuity strip, I would consider something the same, though I also think there's fun from working it into the world you've estbalished if possible, then letting it grow from that. Not every strip I do has to have a yellow or background2 background, after all. :>
DH-01: I know what you mean. The insanity of my comic feels more justified to me because I know it's a regular insanity. :-)
DexX: Your 18 part life story was brilliant stuff, I thought. The important thing abotu serials, I think, is to try and make each part end with a funny, like a daily strip: if you read each piece alone, there should still be something amusing waiting for you. This can make it hard to tell long stories, but I think it helps a strip overall. In your epic, I think you managed that, and it helps it out a lot.