I like all of them, but I'd say exploration is probably my greatest love (though I may be over-emphasizing it due to the fact that it has been out of favor for decades).
I just *love* exploring a world, whether that's a city, or a wilderness, or a dungeon. I like making decisions about how to effectively accomplish my goals (without dying), as well as just wandering around town tasting the local cuisine. The biggest problem that I have is that few DMs spend as time making a world that I actually *can* explore in that manner. I'd actually be fine if I were playing in, say, a 2e/3e era Forgotten Realms campaign with a DM who had a library of old supplements and used them. For example, Lost Mine of Phandelver has Neverwinter on the map, but no information on it--despite the fact that it's a logical place to go to get access to resources you can't find in po-dunk Phandelver. The party in my game ended up going there on a couple of occasions. I have 5 books with information on Neverwinter. A couple of them have just have a short entry, while the other three have multiple page entries--including Volo's Guide to the North, where he explains what some of the major inns are like down to the what foods are their specialties and what smells waft from the kitchen.
So the party is in Neverwinter the first time looking for information on a couple of pesky critters: the flameskull because they couldn't figure out how to keep it dead, and Norm the Spectator, that they felt wrong about just slaying (both because he didn't go hostile on them, and because they weren't sure how tough he was). The cleric of Kelemvor visits his local temple (which I did make up, since I had no info on it) and gets referred to the temple of Oghma (again, of my own creation), and then eventually to the temple of Tymora (yes, I made that one up too). They stayed at a particular inn and ate at particular levels of quality depending on their choice.
On their second visit to Neverwinter, accompanying Sildar as he brought prisoners there for trial, I was able to reference no only the inns, but also the Hall of Justice from the books. I also described the Neverwinter heraldry on the guards, as well as the way the town looked, and the kids that you could hire to run messages around--again, provided to me by the books I have.
I would absolutely love to play with a DM that does that sort of thing. I love the idea of knowing that official lore material is consistently used and not made up just to facilitate the story. If I were in Waterdeep, I'd want to walk around looking at things and have the DM say, "okay, let's take a 15 minute break," while he looked up the section of town we were in to figure out what prominent shops and atmosphere we should be seeing based on the books he had.
In dungeon environments, I most get into the game/competition sort of aspect. Even against other players! Not in the sense of conflict, just in the sense of trying to show how "well" I can defeat the dungeon by playing smart, knowing which risks to take and which not to, and generally being resourceful. I tend to be the guy who throw handfuls of pebbles as a "find traps" device when walking into suspicious rooms, pokes things with my weapon before touching them, and checks the walls before playing with the statue. Dungeon exploration/survival is probably the only part of the game where I actually enjoy the game-like feel of overcoming the challenge. I love one-shots where the goal is to see how long your character can survive the killer dungeon.
As a DM, I really enjoy interaction. I have a pretty wide vocal range, and I'm big into making faces and giving all of my NPCs fairly distinct personalities. Improvisational acting is a talent, so I have little problem coming up with what to say or do as the NPCs. The DMs I've played with are also pretty good with portraying NPCs (even if they aren't as animated) so I get to enjoy this from the player side too, which is good because I really get into my character (as most of the players in our groups do--it's a strength of our role-playing group).
As a player I feel a real need for combat in D&D, probably because we have relatively little of it when I'm not the DM. Our non-combat sessions outnumber our combat sessions by a large margin. This doesn't seem to bother anyone but me--probably because I'm the only one who doesn't play MMOs, and therefore doesn't get fantasy combat anywhere else. As someone who got my D&D start with the old Gold Box computer games, I feel dissatisfied without combats that involve me slaying vast quantities of weak foes. And not just handwaved either. It isn't the same to say, "you kill another 50 goblins" as it is make each of those attack and damage rolls while they swing away at me. (Does anyone else with Gold Box experience remember the pure joy of slaying an entire screen full of kobolds when you first got fireball?)
Okay, I'm done.