I've been playing D&D a long, long time now. I first got it for Christmas back in 1980 - I was already a fan of fantasy and SF, and when I saw the ads for it in Boys' Life and various comics, I wanted to get whatever this game was that let you play out fantasy stories.
Over the years, I've played every edition of AD&D, and a lot of other RPGs besides. 4e is my favorite so far, for reasons that I've already explained over in another thread here on Elliquiy. If I had to take a second choice, though, Pathfinder would be it right now. I can't say that I like what I've seen of Next so far - it seems like an attempt to regress back to 2e, with a few things brought in from 3 and 4e.
As far as worlds go, I started off using Greyhawk, then migrated to my own fantasy world of Tathir, which I developed when 2e came out. I made a lot of conscious changes from the "typical" D&D worlds in it - for example, the main halfling nation is based off of late Imperial Rome mixed with Renaissance Venice, for halflings who love their creature comforts... and their orgies and slaves.
Similarly, having seen far too many worlds where there was 'the' elven nation, 'the' dwarven nation, etc., I had multiple ones of each, with past histories of wars and struggles between them. Thus, the oldest elven nation was ruled by high and grey elves, with wood and wild elves being a peasant underclass, while another elven nation had been founded by wood and wild elves who had fled from there, and did not get along at all with the other. I also strongly dislike the idea of 'evil races', so negotiation and accepting surrenders was often a fruitful tactic - and still is, in the games I run.
After running games in Tathir for around seven years, I got tired of it. Around that time I was growing tired of AD&D as well (this was in 2e days), and for the next several years, I didn't run D&D at all. A player from my Tathir campaign who had moved away started his own D&D campaign up, and I mailed off all my Tathir notes, maps, etc. to him. He's still running his campaigns in it today.
As far as characters go... I have a special fondness for my first character, Victor Ironwolf (and yes, 'Ironwolf' was a steal from Morgan Ironwolf, the example of character creation in 'pink box' Basic D&D. I was 10). He was a ranger, but back then, I hadn't read any Tolkein yet, so I didn't really know what a ranger was supposed to be, and the campaign he was in was very much a Monty Haul game, so he wound up with plate armor, a sword based on Blackrazor from White Plume Mountain, and a pegasus for a mount. In 4e, I finally recreated him - but this time as a warlord, since I really love the concept of that class.
Another favorite of mine is Efindel, a grey elven mage from second edition, who I ran in a high-level campaign, carrying him from 5th level up to 16th. He became an NPC fixture in Tathir as the royal mage of the main elven kingdom, and a guardian of the Gate that was there.
I returned to D&D with 3rd edition, but while I liked most of the concepts behind it, I found the implementation to be lacking, and never developed any characters that really stuck with me. In 4e, favorites of mine have been Victor Ironwolf 2.0, a female paladin multiclassed into warlord named Thornele, and a female mage named Maribelle, who was designed to test how much utility could be gotten out of a mage who specialized in spells that moved enemies around and inflicted conditions on them while doing minimal damage.
Since I've spent most of my time as a GM, though, most of my best stories are about other people's characters and about adventures. Sparran, human paladin of the Protector, and Baal, dwarven priest of the god of Vengeance, who several times nearly came to blows over how to treat defeated foes - even though they were both Lawful Good. The time I told everyone to get out the characters they had that had gotten too high level and which no one would let them play any more (within reason - no characters from people's munchkin days), and ran a campaign that had them roving the D&D multiverse while searching for parts of a gem that was the soul of a primordial god.
Another time, around Christmas one year, when pretty much everyone who had ever been a member of my first gaming group showed up in town, and my friend Craig and I decided to co-GM a party vs. party dungeon. The time when someone in the party made the mistake of saying "Demogorgon", and the GM rolled the appearance chance... and he actually appeared. To a group of seventh-level characters. Efindel only survived that one because I'd been lucky enough to get psionics, and he was able to Dimension Door out of there while the big D slaughtered the rest of the party. And then, of course, Efindel wound up having to go back once he judged it safe, gather up the pieces of their bodies he could find, and go try to find some way to get them resurrected.
I could probably literally go on for hours, and some of my stories would be from this last year - there were some great moments with Victor 2.0 and his cohort, and the players in my current online 4e game have done some very unexpected things, like choosing to kill an Earl's son they got into a bar fight with... but that's really the fun of D&D, and of all RPGs - the unexpected moments, that make you bust out laughing, go "WTF?", or want to pound your head against the table because of how the players are either missing what should be obvious... or have just smashed what you spent hours planning in two minutes with a strategy you never could have imagined.
And at the heart of it, that's why I still play, 22 years later. Because the system or the edition matters a hell of a lot less than the imagination - both your own, and that of the people you play with.