EDIT because it seems to be getting lost: I am talking about wanting to do the whole dungeon fantasy thing, but not with any version of D&D.
More specifically, what do you run when you are done with D&D specifically, but still want something "D&D like" -- dungeons, monsters, traps, treasure, etc...?
I'd recommend looking at D6 Fantasy, GURPS/Dungeon Fanatasy, RuneQuest/BRP/Legend, Tunnels & Trolls, or The Fantasy Trip.
D6 Fantasy is a d6 dice pool, roll & total, compare to TN or opposed roll. Fast and easy character generation. Magic is a little bit construction-set mode. Note that the older Hercules & Xena game is the precursor to d6 Fantasy.
SJG's GURPS and Dungeon Fantasy both can do dungeon crawls. DF is the same core mechanics as GURPS, but I don't know the specifics. I've many friends who have used GURPS for the DF genre. It's 3d6 vs Skill+mods
SJG's The Fantasy Trip is a facelift of GURPS' older, simpler brother. Still plenty good, It's nd6 vs attribute, with n being difficulty typically ranging from 1 to 5, and most combat rolls being 3d.
Tunnels and Trolls has been around since 1975... and the core mechancis are still the same two... Saving Rolls (2d6 doubles open end, plus attribute, vs a TN by difficulty level (TN=(DN×5)+15 ), and the combat roll (weapon's dice, weapons adds, character's adds - in each fight - which may be side vs side, or cluster vs cluster, as the group lets happen, all on one side total, and the other side does likewise, loser takes the difference.
RuneQuest 6e is a flavored setting using a descendent of the 1st ed mechanics, having drifted a bit. It's still recognizably RuneQuest.
BRP (Chaosium's Basic Role Play) is a descendent of RQ 1E as well... but without the Glorathan setting, and being a general RPG.
Legend is (functionally) also RuneQuest - it's Mongoose's RuneQuest II (the 5th edition of RQ), stripped of the Glorantha setting IP. It's the low budget version... There are differences across the line in mechanics., but they're all percetiles, roll under.
While I've not run it, Genisys is a general purpose RPG which can easily do dungeon fantasy. It uses the same mechanics as FFG's Star Wars trilogy (Edge of the Empire, Age of Rebellion, FOrce & Destiny), which I've run extensively (and am about to do so again). It also has a solid fatnasy setting book.... And yes, FFG Star Wars can support dungeon crawling just fine...