I've played all the editions aside from the original 1974 set, and here's what I've noticed in my games:
Basic D&D: This version is fun right out of the box. It's almost board-game like in its simplicity, but allows for many more possibilities than a board game. Characters take almost no time at all to roll up, and there are almost no rules supplements, so there's less pre-game preparation. You just jump right into the adventure. Later versions even had random tables to help stock dungeons, so you could whip up an adventure as you went along. For good or ill, every race and role had a very set position within society due to the race as class mechanic. Elves were all fighting magic-users, and all dwarves were stocky fellow who made good warriors. As these archetypes went along with most traditional fantasy literature roles, my groups and I rarely gave it much thought. bD&D also firmly established the rule of, "when you don't know a rule, make something up" to the point that it was included in the rulebook. It instilled a lot of principles that I still use today, including the tendancy to speed game along by making up rules and then looking through the rulebooks after the session to see if I got it right.
AD&D 1st edition: This was basic D&D with all sorts of bells and whistles thrown in. Some of the rules were recognizable, while others were changed beyond recognition. The strict fantasy archetypes got bent just a little, as you could now have halfling cleric and elves who didn't use magic. The rules as a whole were cumbersome and contradictory, and I think it was generally assumed that you weren't supposed to use all of them. Character creation took a bit longer now that there were more options, but it was still easy enough to jump right into an adventure. The fantasy archetypes were a little bent in this version; you didn't necessarily know if that halfling was a peaceful pipe-smoking fellow or if he was really a cut-throat thief. The expanded options for characters left some folks wondering why they could do one thing but not another; if elves can be clerics, why aren't they allowed to be druids?
AD&D 2nd edition: This expanded the character options a bit more and included skills and specialties that weren't there previously. Character creation began taking longer, making the character more important than the adventure at some points. When you spend over an hour choosing a proficiencies, kits, and later adding the Player's Option stuff, you don't want your character to die in his first session. Adventures seemed to get easier in order to allow the PCs a better chance at survival. As the options continued to expand, the limitations of the system became more apparent; if you could have an elven demi-bard using the elven minstrel kit, why couldn't you have a normal elven bard? 2nd edition also changed the name and cultures of demons and devils, which hacked a lot of people off but also fleshed out the concept of the Blood War and gave a great deal of culture to the planes.
D&D 3rd edition: The character options of AD&D 1st and 2nd got cranked up to the max here. Old limitations were removed entirely, so now you can have virtually any combination out there. The old archetypes are pretty much all gone; there's nothing saying the dwarf in front of you is a stout-hearted warrior instead of a weak wizard. Characters have more powers and abilities than ever before; a ranger can disappear right before your eyes, and a even a fighter has near-supernatural talents. The world is much less human-centric, since humans are no longer more versatile than any other race. As a result, many worlds are higher fantasy than before; there's no reason elves won't be selling their wares in the streets instead of practicing arcane magic in a secluded forest. The addition of feat prerequisites and prestige classes makes adventuring almost a career path; you build up to a higher goal rather than just letting your skills progress as they may. A faster experience track ensures that inexperienced characters like Frodo Baggins or Taran from the Prydain Chronicles won't be inexperienced for long. Monsters are bigger, badder, and now just as unpredictable as a PC. While some aspects of the game, like demons and devils, have returned to their 1st edition roots, the culture and detail given by the 2nd edition is also included.