Why do you play 4e rather than another edition? Alternatively, what do you like about it even if you mostly play another edition?
(Yeah, this topic has undoubtedly been covered before; just humor me. It's for a charitable cause.

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I'll humor you because I enjoy discussing why I like/love certain things, gaming being one of them.
I have run games of D&D since Moldvay Basic. In that time the edition I've used the least was 2e, mostly because of time. When 3e came out I ran a continuous campaign that ended in early 2011. When 3.5 came out we eventually changed to it mid-campaign. I've been running 4e since after DDXP in 2008, though my main group started playing it regularly in July 2011 (we had a lot of games to play in that time between long term campaigns).
I love to run 4e because it gives me a great amount of freedom to improvise, and "break/bend the rules" without breaking the system. It gives me a solid rules framework from which I can easily expand, or contract pretty much at will. I also like a lot of the flavor that was incorporated into the game by books like Plane Above, Plane Below, and particularly Heroes of the Feywild. A lot of the flavor enhances the game without impinging on the mechanics. Which easily let's me reflavor to taste, or change mechanics as warranted.
I like that my typical preparation for games is now involved with the "story" instead of the "mechanics". My preparation time needs have been cut significantly. While running the game I love that I only need three things in front of me; dice, the DM Screen, and the adventure in front of me. I don't have to go look for explanations of spells, or creature specifics except in the text that I'm using to run the game. The noteworthy exception to this are rituals, which are heavily used in my campaign. But usually I don't have to look those up since my players have the text right in front of them.
I really enjoy monster creation and modification. It is so easy to create "unique" creatures that work as you want them. I can take a piece of "lore" and turn it into an interesting creature, usually within minutes.
I also like that the game gives me multiple workable ways of rewarding the PCs without having to make up ad-hoc rewards that might, or might not be appropriate. It lets me keep the focus on what the players want their PCs to do, instead of what I would want them to do.
I particularly love that the game gives me a solid foundational framework for when the players want to do something not particularly covered by the rules. The framework doesn't necessarily give me a solution, that has come with experience just as in previous editions, but it does provide me with mechanically appropriate ways of dealing with the situation. When I do have to make things up, I can usually use an existing mechanic and expand it, reflavor it, and put it into play with very little concern for what it will break as a knock-on effect.
As a player I like that it gives me the freedom to reflavor my character as wanted, while at the same time continuing to provide interesting options that don't make me feel like I've been left behind. As an example, there is no "swashbuckler" class in the game. However I was able to reflavor the ranger class to be a pretty good substitute. I could have done that with the Fighter, or the Rogue depending on the particular flavor I was envisioning for the class.
I also love it because it's the first edition of D&D that my wife actually didn't require involved explanation of the rules to play in. She got into it with very simple instructions. We had been playing a low level 3e adventure and she remarked how much easier it was for her to pick it up with 4e.
In short for me, 4e provided a much richer, fully realized, and easier to play game experience out of the box than anything that had come before, except for Moldvay Basic (ease only). The things that it didn't provide easily out of the box, I was able to "fix" for my campaign without breaking the system.