I have several that stick out to me. Hard to choose a winner here:
-Wolfen by LWM
--This is one of those mods that gives me a taste of how other weapons would feel in Hexen. Not to mention the aeon mana system completely altering how I play certain character classes. Now if only the boss fight wasn't so anticlimatic, it'd have been hands down favorite experience in ZDoom thus far.
-Warzone by Xaser
--Soft spot here for mods that pile on guns after guns after guns. Dat chaingun though.
-Shooting Monsters with Weapons/IWAD
--Okay that's actually two different mods but they both incorporated something really fun in them- dual weapon wielding.
For vanilla, I have to go with the classic uac_dead.wad. An oldie but goodie, also the first use of self-referencing sectors for an invisible stairway. Momento Mori comes in a close second for being a pretty good 32 map set (accompanied by completely new music, to boot).
For ZDoom, that's a bit tougher. As good as KDiZD can be, I find the levels to drag on far far too long even when you know what you're doing, where even those most optimal paths to take feel inefficient. TeiTenga is a pretty memorable one (another oldie but goodie), being one of the early ZDoom wads that made heavy use of scripting. I'm not sure what I'd call "favorite", though, as ZDoom's capabilities allow for mods to cover separate niche areas (Metroid Dreadnought is probably a "favorite" gameplay-altering mod, but how can you compare that to something like Wolfen, and how do you compare that to something like Serpent Resurrection?).
I know it probably sounds like either a cliche or I'm trying to be funny but I think that doom.wad is probably my favourite. There are WADs with bigger maps, that are more technically proficient, provide better fights etc etc etc but for whatever reason (and I accept that nostalgia may well be a big part of it) the original three episodes of Doom, to me, are fantastic and nothing gives me that Doom feeling more than playing them.
Probably the original Titan by Ixnatifual. It's most likely down to the impact it had on me, being the first port-specific mod I ever played, but there's no denying that the final battle was much more satisfying than D2's ending.