I don't know whether many players spend time thinking about what they want from a classic Dungeons & Dragons campaign: they might just show up, happy to be at the table and eager to be fed whatever you've cooked up for them, chef's choice. By classic, I mean a campaign in the archetypal style with kobolds, smokey taverns, dungeon crawls, torchlight, pit traps, fireballs, wizard towers, orc armies, undead, treasure chests, dragon hoards, evil cults, bags of holding, and potions of healing. At least in my experience, aside from the obvious ingredients of hanging out, dice rolling, problem solving, and monster killing, I've come to find there are a few fundamental extra things that can be added to really enrich the flavour of the classic campaign.To that end, here are some not-so-obvious ingredients to add to the players' pot:
Something cool for their characters to get
Players love to acquire loot, whether they steal it, have it gifted to them by an important NPC, or take it from the body of a slain foe. The more unique and difficult an item is to acquire, the more they'll value it. Magic items are especially desirable. The cooler the better.
Some deed on which to build their characters' legends
Players want to gain fame and notoriety in your world. They want to achieve things nobody else has achieved, things that will go down in history. They want to accomplish deeds which are unique, one-time events. They want to kill Smaug, and be remembered for it. They want to rescue the princess, and be remembered for it. They want to become legends.
To make dramatic choices that change the game world
Players want their choices to matter. They want to know that because they chose to spare the evil wizard's miserable life, the world turned out much differently for it. They want to see the village they saved grow and flourish. They want the ties they helped form between two kingdoms to lead to an alliance against the oncoming horde of orcs. They want to affect the world around them.
To meet NPCs who come to value and depend upon them, or who come to fear and respect them
Players want to build relationships with NPCs. They want to earn the trust of the haughty elven professor at the arcane university. They want the shrewd desert merchant to hire only them to guard his precious caravan. They want the arrogant leader of the Thieves Guild to learn not to mess with them. They want to be feared, loved, respected, accepted, valued, and considered by the people who live in your game world.
To have unique and vivid experiences through adventure
Players want to be awed by the fantastic. They want to have their minds filled with images of grandiose architecture, strange creatures, and unusual landscapes. They want to be thrust into situations that couldn't happen in the real world, probably involving dragons, magic spells, and otherworldly civilizations. They want to have novel experiences they can't find anywhere else.
To be surprised
Players want to be surprised. They want to say "I didn't see that coming." They want to cry out "Whaaaat?!?!" and "Ohh shiiit!" They want to wonder what they're going to find around the next corner. They want the king to transform into the werewolf they've been hunting. They want the pink potion to do something unexpected when they quaff it. They want the statue to start speaking to them when they walk past it. They want some of their guesses to be wrong.
To go through a transformation
Players want their characters to change. They want to start off the game as one thing, and by the end have changed into another. They want to increase their power, going from level 1 to level 20, from poor beggar to rich baron. They want to change their personalities, starting off as mistrustful and reserved, and coming to depend on the party and think of it as family. They want to rise from bad apple to charitable protector, or fall from righteous do-gooder to selfish bastard. They want to claw their way from peasantry to knighthood, becoming noble leaders. They want to undergo an alchemical ritual which will permanently turn their eyes yellow, making them frightening to NPCs but giving them the ability to see any residue of magic. They want to forge who their characters are through transformation.
To learn secrets
Players want to be in on secrets. They want to feel they know something other NPCs do not or cannot know. They want to know the royal advisor's true identity. They want to know the secret way into the forbidden city. They want to know wizards are actually real. Knowing secrets makes them feel powerful, part of something special. They want to hold the truth in their hands.
Items, Deeds, Choices, Relationships, Experiences, Surprises, Transformations, Secrets. These are the subtle ingredients hidden in the pot I think a lot of players enjoy in D&D, like a blend of spices which makes someone go "Mm! What is that?" Sometimes it happens by accident, like a miraculous one-off dish, but consciously including all of these ingredients can lead to some pretty satisfying games in my experience.
May this inspire you and give you food for thought.