Dungeon’s and Dragons is kind of reaching the point of being a generic name for fantasy gaming. I see it that way, or perhaps more specifically as combat spelunking if I’m really focussed on the dungeon aspect.
There are an embarrassment of riches in the the fantasy RPG space, and some I enjoy have been mentioned already - Dragonbane, DaggerHeart and Shadow of the Weird Wizard. GURPS Dungeon Fantasy, too.
Another game I really enjoy in this space is Savage Worlds, and that could be just using the core book, or adding in the Fantasy Companion or even using Pathfinder for Savage Worlds for a very close analogue to have D&D type games feel.
Each of these options gives a different spin on the core fantasy RPG feeling. Savage Worlds would be my base choice since it is still my favourite system overall (and it has a pulp fantasy vibe). But if I want something more gritty I might go with GURPS Dungeon Fantasy or Dragonbane. If I want something a bit more baroque then Weird Wizard. DaggerHeart is the new option and I’m still fully working out how that fits into the picture.