Alright, so during 5th Edition's playtest Mearls and the developers put a large emphasis on getting the "feels like D&D" right. Although the game seems to have its good and bad points, it can replicate traditional dungeon-crawling relatively well.
But getting the feel of an RPG right is subjective, and given the 40 something years of iterations Dungeons & Dragons went through, you have entire player bases who grew up with what as well might be entirely different games.
So I posit to you folks, what feels like D&D to you? It doesn't have to anything concrete; it can be specific rules, themes, settings, characters, races, etc, whose inclusion is an important part of of the RPG.
What feels like D&D to me:
Race, Class, and Vancian Spells: Such archtypes are huge factors in character generation. They're so omnipresent that I can guarantee to find them in just about any sourcebook or Edition.
Dungeon Delves: Call them ruins, call them Underdark caves, call them them fortresses of evil. Making your way through an enclosed hostile space full of adversaries and treasure is a big part of the game.
Big Worlds: Many campaign settings are highly detailed, full of all sorts of places to explore. While games set around a small locale can be done (Ptolus), I've come to expect most D&D games to have big wide worlds for your PCs to stomp around in and get into trouble.
Cosmic Forces: Gods, religion, and the planes have a more direct affair in the worlds of D&D than most other fantasy settings. Evil as a tangible force which corrupts, deities who choose mortal vessels to channel their powers, and obvious marks of the otherworldly permeate throughout.
Adventure Paths and Sandboxes: There's a lot of adventures for many different games out there, but these two styles were popularized by Dungeons & Dragons and continue to be common trends. The adventure path is a linked series of adventures which often take PCs from "zero to hero" status, starting out as humble folk who become legends in their own right. Sandboxes are non-linear adventures akin to D&D Elder Scrolls; sure there's an overarching plot, but you have a whole world to explore full of dungeons, locations, and side quests unrelated to the main plot.