In casual rounds with my two regular buddies, we are pretty liberal about picking up short putts. We've played with each other enough and often like to play several rounds a day, so those gimmies are OK with all of us (none of us are as OCD as it seems that a lot of people are). That said, if I'm playing with people who I am less familiar with, I putt everything out.
In tournaments, I don't think having a "gimmie zone" makes any sense. From a pace of play perspective, I think a bigger issue is most players' insistence on putting strictly according to who is away, even if everyone is inside of 10'. I always tell my cardmates that they should feel free to putt out or drop in their park job, and I will ask the first time I'm that close if anyone minds if I drop it in while dude over there is figuring out which putter he is going to use for his 30 footer. It drives me crazy to see two or three guys standing there looking at each other trying to figure out which one is away and should putt first when they are all between 3-5 feet away from the basket...
A related tournament pace of play thought - I wish everyone didn't insist on taking their disc out of the basket before the next person putts. Sure, if it is hanging in the chains it should be moved but if laying flat in the tray just leave it there. There have been many times in a tournament round when the guy who putts before me makes it and starts to go to the basket and I will tell him to leave it, and he looks at me like I have two heads. Let's keep it moving, people. Ready golf would go a long way towards making tournament rounds more tolerable.