When the original Dungeons & Dragons was released back in the 1970's into the mainstream, players were treated for the first time to open exploration of tombs, underground caverns, and fortified compounds. Today's adventures call for lots more complexity as the game of D&D has grown and evolved over the years with different generations, different publishers, and different pop culture phenomenon. However, there's something to be said for those old exploration adventures like Tomb of Annihilation or the earliest incarnations of Greyhawk. Though simpler in terms of goals for the players, there was an immersion and complexity to those old modules and settings that encouraged more free-thinking exploration, and it's sadly something that a lot of modern adventures lack. However, there's a way that we can have our cake and eat it too.
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Look, there's absolutely nothing wrong with running your campaigns that have complex story arcs or your adventures that play like episodes of television shows. However, part of the fun of D&D, especially for players, is interacting with the world around them. If the Dungeon Master is the one who subtly or not-so-subtly guides the players on a course of action he or she wants the players to go on, my suggestion to that DM is to instead write a book. Trust me, I'm both a DM as well as a published author and I completely understand the drive that many DM's have to tell a good story because I have that drive all the time, and sometimes I struggle with not inserting all the cool ideas I have into the games I run. D&D is a game, and the players are supposed to help guide the narrative, and part of the way we've lost the exploration aspect of the original D&D is that we feel the players will be bored just having their characters explore dungeons, encountering shambling skeletons, slimy oozes, or terrifying and mighty dragons. But it doesn't have to be that way.
One way to spruce up an original dungeon crawl is to put those story skills to good use as a DM and come up with a thorough history and explanation for the existence of the dungeon, crypt, or stronghold the players are exploring. Give it a unique purpose, populate it with both familiar but also new and interesting enemies, and really let the players get back to the basics of using their characters skills and abilities to help guide them on their way through the darkness. The story of the actual history of the dungeon may never come up or be important to the players, but as a storyteller, the history you concoct for the location will play a huge part in helping you make the place feel more real and alive. Just knowing a bit of its history will even subconsciously help make the location feel more tied together and tangible for you and the players alike. And who knows, maybe with the right amount of exploration, the players might uncover the history as part of the quest, or as a detail that may help them on a different quest.
Another way to spruce up dungeon crawls are with puzzles, traps, and monsters. Make sure to give the players a chance to solve the puzzles on their own through checks, and not necessarily solely by roleplaying. Sometimes the PC's are more intelligent than the players are themselves, not in an insulting way just based on who they are as a character. After all, the party's resident wizard Thelias the All-Knowing must be extremely educated, dedicating his life to learning whereas his player Grant may have never attended college in real life, but that doesn't mean Thelias' knowledge is only limited to what your average person knows. Allow them to use their checks to help if they can't solve the problem in real life.
With traps, you want to also give the players a chance to see what the traps are and how deadly they can be without resorting to having them step in the worst ones right off the bat that could result in a TPK. Introduce the concept of traps early on, and get the players into the rhythm of checking for traps often, or trying to disarm them, so they have a chance to sidestep them completely or render them harmless. This will make the players feel accomplished, but if they're hurt by one every so often, they will have to expend much-needed resources, resulting in the players feeling a sense of urgency as they explore. Remember: Players have lots of tools in their traveling packs that they often don't use, that are specifically for dungeon exploring such as rations (there's no hunting in dungeons for the most part, so they should actually use their rations while inside dungeons), ten foot poles, caltrops, rope, pitons, and other useful tools.
Monsters should be interesting and have a reason for being down in the depths. Don't just throw random beasts at the players that don't make a whole lot of sense for being down in a crypt. Have a reason for it, even if it's just in your head, because that reason may present a role-playing or adventure opportunity down the road.
Overall, give the players a little more agency back by bringing them back to D&D's roots - exploration. Keep your plot, keep your story threads, but open up your mind to deviating a little bit from the planned path and let the players help you craft a tale worthy for a king. - Joe