So I'm seeing a pattern here (which oddly, I wasn't looking for in the  thread I started on a similar topic back before the crash--a slightly  different focus can bring out interesting ideas). So far, the categories  look like:
1) Homebrew with Selective Borrowing: You see the  published material mostly as inspiration for creating your homebrew  world. If you keep to a theme or a map or something you consider  important, you consider your game to be a <Insert Setting> game.
2)  Alternate Universe Setting: You start with all of the assumptions of  the published world (according to whatever materials you have available  to you) and then selectively make massive changes to a variety of  things, which might include well-established world assumptions, maps,  races, NPCs, past timeline, maybe even playing with a different ruleset.
3)  Canon with Selective Changes: You start with all of the assumptions of  the published world (according to whatever materials you have available  to you), and assume anything that doesn't come up during your campaign  adheres to those assumptions unless otherwise stated. You make selective  changes to parts of the world you feel should be changed to better fit  your personal vision, including past timeline, NPCS, and other  relatively minor elements. Alternately, you might stick closely on  pretty much everything with One Big Change (like One Big Lie on Mohs  Scale of Sci-Fi Hardness).
4) Temporally Fixed Canon: You start with  pretty much all of the assumptions of the published world as of a  particular date--timeline or product publication--or you accept all of  the canon from certain foundational materials but not others. Anything  after that date or outside of that product set can and will deviate due to the developments of your  campaigns or DM's (meta)plots.
5) Established Canon: You follow all  of the assumptions of all of the published materials you have available  as closely as possible. Naturally, once a campaign has begun, things  will deviate from ongoing official canon as in #4, but you attempt to  keep up with ongoing canon and implement any elements that you can.
I  generally go with #3, with leanings toward #4. I set a date whereon  canon up to that date is generally assumed to be correct, but I make  subtle changes--most of which are invisible to players not highly  steeped in the lore. I welcome input from players who might know more  about a setting than I, with the caveat that I might over-rule any  element I dislike.
Here are selected examples from this thread of each of the types. Correct me if I'm wrong.
	
		
	
	
		
		
			When I talk about running a GH game, or an  Oriental Adventures game; or when I say that I am running a module; what  I mean is that I am using some maps, some characters, some tropes and  themes, taken from the setting or module.
But I don't pay much attention to the "canon" of the setting or module.  I've run OA using homedrawn maps and the Kara-Tur boxed set. I'm  currently running a GH game, using Burning Wheel mechanics, and I move  between my old folio maps and 2nd ed and 3E era ones - whichever happens  to be at the top of my folder - without worrying too much about it.
What makes this game a GH one is the basic geography and history (Hardby  is a city ruled by a magic-using Gynarch, across the Wooly Bay from the  Bright Desert, which is populated by Suel tribesmen). Not the minutiae  of canon: the details of the setting I make up as needed for play or  determined during the course of play.
I approach my 4e games - one using the default cosmology (but the "world  map" is the map from the inside of the old B/X module Night's Dark  Terror) and one in Dark Sun - the same way. Follow basic outlines, and  use published material where it seems useful, but otherwise without too  much concern for what is "canon" in the setting.
		
		
	 
I used the above to define #1.
	
		
	
	
		
		
			I often create an alternate version of the  setting. In my FR, the sundering was very different, for instance.  Netheril is still a power, but has mostly ditched Shar as bad deal, Myth  Drannor is still intact, there are still earthmotes floating around.  Returned Abeir, all the Genasi and Dragonborn, etc, are mostly still  there, and aunt her is back, but greatly diminished, because I don't  retcon away the fact that Tymanchibar sat on it. Instead, the two worlds  were aligned very closely for about a month, and moving between was  very easy. This lead to the Unther contingent that was on Abeir to come  back, and use the chaos to take "back" a large chunk of their old  geography. Except, it's not the same land. 
Netheril no no longer has flying cities, but only Shade is gone. The  other one is nestled into some mountains, it's once great magic now used  to keep the desert at bay. Post war, they are eager to put the past  behind them, and the other nations are mixed in their response to that. 
 
Sembia, Netherl, Cormyr, Myth Drannor, The Dales, and some other groups  in that area have formed an organization of Knights, which include a  handful of orders, ranging from Paladins, to corsairs, to ranger-types,  and swordmage types, attached to a school on the southern Dragon Coast.  Both organizations are international, and partner nations send the  children of their most powerful families there, as well as recruited  commoners and petitioners who prove themselves. 
Recently, (ie, the year my current campaign is starting) students from  many new nations are enrolling, and the school is being expanded. its  built into a canyon, where it opens into the ocean, with earbtmotes  having been moved to hover between the cliffs. 
A new knighthood is also being formed, that will bond with and ride on the backs of giant birds
		
		
	 
I'd say the one above is #2.
	
		
	
	
		
		
			I like to keep up with the Forgotten Realms and  its lore, but I don't mind changing things around. As in art, you should  know the rules before breaking them. If Luskan becomes a halfling  village in my campaign, I want it to be a creative decision and not pure  ignorance.
		
		
	 
Hard to say due to brevity, but this one above seems to lean toward #3. See my own example at the beginning for another #3.
	
		
	
	
		
		
			Importance of canon and  what I consider canon depend upon the setting in question. Canon is also  only important for establishing the base setting and lore (pantheons,  races, cultures, etc.). It is to be diverged from once play begins.
Greyhawk: It is the original folio, original boxed set, the deities  Gygax presented in Dragon Magazine (so no Suel Pantheon), and bits of  information on various cultures that appeared in Dragon (e.g., the  culture information that appeared in the Barbarian class).
Forgotten Realm: Canon for me is the original grey box set, the 1e FR  series of supplements, some early 1e articles by Ed Greenwood, and a 2e  supplements from the 2e FOR supplement line.  Nothing from the Time of  Troubles onward
Al Qadim: Arabian Adventures book, Land of Fate boxed set and anything by Jeff Grubb
Darksun: Only the original boxed set and 1e articles by Timothy Brown
Ravenloft: Only the Realms of Terror boxed set and a few of its supplements.
Furthermore, any additional canon added by Planescape, Spelljammer,  novels or late 2e and beyond is automatically ignored by me.
		
		
	 
The above is a perfect example of #4, I believe.
	
		
	
	
		
		
			I care deeply about canon right up to the start of a campaign. The point of using a setting, rather than making it up on my own as I go along, is to provide answers to questions about the world the characters live in at the start of the campaign.
But once the PCs start actually doing stuff, my concerns firmly fix themselves to that stuff and how it changes the world around them, and if it isn't compatible with some bit of canon - especially a bit of canon that comes along in a published product released sometime during the campaign - then it is the PCs actions and their consequences that stay true.
Also, there is one special circumstance in which I care not the slightest for canon and toss it entirely to the wayside: if a player knows it better than I do and tries to dictate to me along the lines of "Um... didn't you mean [this]?" while we are at the table trying to play the game.
		
		
	 
The one above seems to me to be a #5.
In addition, I would add one more category:
6) The Strawman Canonist: You follow all of the assumptions and elements of  the published materials, making sure to acquire as many resources as  possible to avoid missing anything. Once a campaign has started, you do  your darnedest to make sure nothing that happens contradicts current or  future products that are/will be coming out. (I don't believe anyone  actually does this, but I get the feeling that sometimes it is used (I  would say misused) as an example of following canon for contrast with  going more free-form. I would say #4 and #5 are better actual examples of  following canon.)