The term is certainly problematic and more individualized as has been noted here, so as someone who claims "old school" preference I will only note what I think makes me fit this category and try to identify the central elements that really bind us or separate us:
1. It's neither bad nor good, but there is an age difference at play here - I consider myself "old school" for one because I remember days before FLGSs and Amazon where we (in the late 70's and early 80's) would go to Walden Books or other local bookstores looking for those shrink-wrapped Modules, and had to save up for the "expensive" $25-$29 books like the DM's guide. Yes, this is a bit of ego here... but there is a separation with those who remember TSR and Judges Guild really as the only games in town and the mass of material that came later.
2. Basic medieval setting vs. others. I would say "Old Schoolers" liked the medieval as basis for what was known as "D&D," and liked their other forms separated (i.e. Gamma World or Star Frontiers). My impression is that "new schoolers" like much wilder variety and mixes of genres in their games.
3. Slow, varied character progression vs. fast, uniform player progression. "Old schoolers" liked the varied XP charts and slow progress (it could take months of games to go to 5th or 6th level, and characters advanced differently), while "new schoolers" want the fastest routes to 20th level and decry varied leveling.
4. Archetypes vs. Fantasy "Superheroes." My own preference and what I think applies to many is the idea that PC's were classic fantasy archetypes - the Fighter, the Thief, the Magic User... and enjoyed creating the differences in a game out of WHO they were rather than WHAT they could do. My look at 3.x and other modern RPG systems (and I played 3.0 for 4 years) would indicate that the emphasis is on heavily empowering characters to be "Fantasy Superheroes," able to very quickly display enormous feats (pun intended) of skill and combat. All this isn't to say one is better or "right," these are just the different points of view. WotC very smartly has marketed towards the latter, and looks to continue to do so with its future. This particular comparison is also the spark of difference when discussing Artwork under these terms.
5. Rules light vs. Rules heavy - I think is the defining separation - those who prefer having broad strokes to fill in (and the one common denominator for all the "old school" modules was that they were NOT as absolutely specific to setting, even when nominally set in Greyhawk, and always needed a DM's own additions) vs. those who want lots of "crunch," detail and specifics. I play C&C, and recently came across a review that stated "unlike the claim on the cover, this is not a complete system.... rules have not been provided for any number of situations." This in a nutshell is the real difference - for "new schoolers" do not see the "essential rules only" approach as "complete," and want as much as possible provided.
I also think some "old schoolers" tended to use or not use miniatures, and if they did these were more as accessories rather than integral parts of the campaign (unless playing Chainmail). I have played for over 25 years, and have never used miniatures. "New schoolers" (again just my opinion) find it hard to not see how to run a combat without a table-top layout and the minatures. This is what the rumored 4.0 is going to probably gear towards, if the leaks prove true.
Again, take all this with a grain of salt - my opinion is that you should enjoy the game whatever way you wish to play, and my own preferences are simply that - my own. I claim to be "old school," but that doesn't mean to imply "better" or "right," and the folly we fall into is somehow wanting to find vindication that any one way of RPGing is somehow "superior" or more proper than another. I've seen thread after thread bashing Gary Gygax, some of them quite mean and vitriolic, just because he's said he doesn't like modern D&D. Does it matter if you do? It's almost as if people want to hear the more well-known personalities (especially the "father" of D&D) validate that what they are doing is "correct" - which is a little ridiculous. Stop worrying about what everyone else thinks and RPG in whatever form you enjoy.
It is, after all, a
game .