I heartily second the Guild games on the 3DS, specifically:
Crimson Shroud,
Attack of the Friday Monsters and
The Starship Damrey as they are all quite atmospheric games and
The Starship Damrey in particular sounds very similar to
The Fall (/Metroid) that you describe (sorry haven't played
The Fall myself).
Weapon Shop de Omasse and to a lesser extent
Liberation Maiden from the Guild series are good games, but not sure if they really fit your criteria.
Art of Balance on the WiiU is a good puzzler, but isn't a "classic" per se. It's also just a series of puzzles so obviously not a whole lot of atmosphere
.
Azure Striker Gunvolt and
Shovel Knight are both really good Mega Man-style platformers.
Shovel Knight is similar to the older NES Mega Man games, while
Gunvolt reminds me more of the SNES Mega Man X games. I think
Shovel Knight is the better game for what it's worth.
Both of the
Gunman Clive games on the 3DS are two of my favorites for the system. They control
really well, have a unique art style and they're both super cheap (and short).
Cave Story is also available on the 3DS (I'd just get the cheaper non-3D game, I don't think it adds that much for the jump in price) is a pretty good Metroidvania-ish game.
Guacamelee is also a solid, similar style platformer that is on the WiiU (and maybe PS3/360? I don't remember). However, the best Metroidvania-style game on the consoles you listed is
Shadow Complex (XBox Live Arcade) and is fairly similar in tone to the Metroid series.
SteamWorld Dig is yet another Metroidvania on WiiU and 3DS but I think
Shadow Complex is your best bet here.
Bastion and the developer's more recent game
Transistor are phenomenal games. I'd maybe give the edge to
Bastion as it is definitely one of the crowning achievements of indie scene.
Bastion is available on X360 but not sure about
Transistor are available on X360 or PS3.
Brothers - A Tale of Two Sons is a pretty, atmospheric, story-driven game. I enjoyed it quite a bit and I believe it's available on both the 360 and PS3.
Child of Light on the WiiU is another atmospheric RPG with great art style. The combat is turn-based and plays like the ATB system from the older Final Fantasy games. The rhyming gimmick in the game is obnoxious and not very well-written, but doesn't detract too much from the game.
Journey on the PS3 is fantastic game that is all about the atmosphere. Same with
Flower although that one is much more of a casual, pick-up-and-play for a few minutes relaxer. Avoid
fl0w, however, that is from the same developer. I loathed that game.
Fez, I haven't played much of but I enjoyed the short amount I did play. It's most certainly one of the most recognizable indie games. It's available on just about every platform. Same with
Braid; these two are considered two of the classics.
Limbo is also another readily available retro-platformer-with-a-unique-gimmick that I unfortunately haven't delved much into. All 3 games have a pretty good sense of atmosphere.
Super Meat Boy is a great, hard platformer that is based around 30 second to 3 minute long stages that you are constantly killed on until you finally beat the stage
.
Protect Me Knight is a fun multiplayer game that is similar to old top-down Gauntlet. The first game is available on X360 Indie section for like $1 or whatnot. The sequel was supposed to be coming out for the 3DS but I haven't heard anything about it for a while now.
Binding of Isaac is a Zelda-style top-down dungeon crawler. I haven't been able to get into it myself, but it is a very popular and well-received indie game that I believe just got a release on the WiiU?? It's from the
Super Meat Boy team.
Rogue Legacy is amazing. You should buy
Rogue Legacy. Everyone should buy
Rogue Legacy.
Spelunky was too hard and esoteric for me, but is well-regarded for those that can.
The Swapper is a great puzzle/platformer with oodles of atmosphere on the WiiU.
Teslagrad is also another pretty good puzzle-platformer as is the
Trine series (although the latter is more of sidescroller beat-em-up/puzzle fusion). Both are on the WiiU as well.
Terraria is like a 2D Minecraft. Not personally for me, but it (again) is incredibly popular and should probably be given a look.
Luftrausers is a fun arcadey schmup with really good music. It's on PS3.
The
Shantae series on both 3DS and WiiU are popular, but I haven't tried them myself.
The Unfinished Swan on PS3 is one that I just started playing and it definitely is a game that the main goal is exploration and atmosphere. I've quite enjoyed the few hours I've put into it so far.
Those are the cream of the crop from my perspective from what I've played (and heard).
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. I remember having to start over after the first Ultimecia (sp?) fight because I just could not beat her because my character builds were garbage. Also, I now feel really old now realizing that game is over 15 years old! 
