For those who never played the original, just skip to Binding of Isaac: Rebirth, it's better in every way. I've sunk just over 300 hours into it, and will likely sink 200 more once the Afterbirth DLC is released.

I'll add some multiplayer/party games that always get a play at LANs:
Starwhal
Nidhogg
Gang Beasts

This War of Mine is a very heavy game.  You have to manage your character's mental states as well as simply keeping them safe, warm, and fed.  You need to do things that will cheer them up.  Some characters are rather selfish while others really care about others a lot and are easy to damage.  When playing with only one character (which is unusual, as you usually have three or four), you have no one to defend your home from looters while you're out scavenging, so they will get depressed when people break in and steal things.  I didn't really know what I was doing and left him depressed for too long and he hung himself.  It was pretty shocking.

When one of your characters gets killed or dies from illness, that's it, they're gone for good and you're left with whatever characters you have left.  Though, sometimes, someone else will knock on your door and ask to join your group.

I own Limbo but I haven't played it, as I don't really care for platformers.

I literally can't recommend it enough. You will look back at the original, and wonder how you ever played it :P

Also, a free update for the original is out, with new mental bosses and a true hard mode. Unfortunately, I cannot go back after playing Rebirth.

Nice thread :)

I've had something of a love-hate affair with "indies" over the last few years. Some of them are far superior to their big-budget cousins, even with a small team of developers operating with an even smaller budget. Others are long on style but short on substance, and oriented around a high-concept idea rather than a strong set of mechanics. As with all genres and corners of the video game industry, you need to know where to look.

Some of my favorites:

Retro City Rampage (PSV) -- I first played this game on a lark, but soon fell in love with it. The retro pixel graphics are charming; the gameplay, built around a true open-world, is diverse and engaging; and the pop culture gags are hilarious. 

Guacamelee (PS3) -- It's not easy making a great "Metroidvania" game, but the team at DrinkBox did so with panache in Guacamelee. What sets Guacamelee apart from others in the sub-genre is its deep combat system and its deliriously difficult platform sections.

Braid (X360) -- Braid could easily have fallen into the same trap that has ensnared so many "indie" games -- a preponderance of plot -- but designer Jonathan Blow wisely focused on puzzle design and time-manipulation mechanics. The result is a challenging, innovative take on puzzle platformers and one of the defining independent games of the seventh generation.

Castle Crashers (X360) -- I'm a sucker for co-op beat-em-ups, and Castle Crashers is one of the best. With a wicked sense of humor, refreshing art direction, and huge replay value, Castle Crashers is required playing for anyone who grew up with Final Fight, Streets of Rage, and Teenage Mutant Ninja Turtles.

Katawa Shoujo
Sunrider
Defender's Quest
Xenonauts
Dead State
Shovel Knight
UnEpic
Sword of the Stars: The Pit

Katawa Shoujo is a very well made PC Freeware Visual Novel. While being strictly speaking an eroge, it deals with physical disabilities with the utmost respect. Every character, even the main one, has some kind of disability and explores how each of them cope with them and how they go through their daily lives without discriminating or white knighting.

Sunrider is also a freeware Visual Novel on PC, and mixes it up with pretty hard turn-based battles in Space with cruisers, battleships and mechas called Ryders.

Defender's Quest is an RPG/Tower Defense mix which can become quite challenging, especially if you go for 100% completition.

Xenonauts is a reimagination of the first X-Com titles but set during the cold war, and with the same difficulty levels as the old titles. Very well made but extremly difficult.

Dead State is a Turn-based tactics/resource management & exploration game during a Zombie Virus outbreak. Nice story and characters but a bit buggy.

Shovel Knight... do I really have to tell you what this is?

UnEpic: A side-scrolling Dungeon crawler with tons of references to other games or TV series, but delivers them extremly heavy-handed (half of them got cut out after the rightsholders of these complained anyway). I love it's Zelda II style gameplay, though.

Sword of the Stars: The pit (short: SotS:TP) is a modern take on classic top-down roguelikes, complete with their difficulty level and random dungeon generation.

Dungeon Defenders
Terraria
Rocket League
Don't Starve
Rouge Legacy
Hotline Miami
Binding of Isaac
FTL
Unfinished Swan
Journey

I played Journey and that game jerked a tear out of me. The very last section was extremely immersive and "spiritual" because of sensory deprivation. It was bazaar in a good way and sublime at the same time. The story and the world were interpretive, of course, but the clothing and setting were inspired by the middle eastern culture, and it was interesting to witness outside of war games.

Shovel Knights' artistic design mimics that of 8-bit games, but it still borrows a lot of graphical design tricks from games that came on stronger hardware like the moving background, memory constrains on the numberof objects on the screen, ect. It played like that classical era never went away but it still incorporated some modern design choices. The Platforming is accurate and solid, and the levels were short and tightly designed. The dialogue is cheesy but appropriate and it actually has a compelling non-obstructive story and interesting symbolism.

Rogue legacy. A metrovania with a randomly regenerated dungeon. The game relies on simplicity and has a ton of upgrades but the difficulty is used to artificially extend the length of a rather short game. The story is told through a journal that pokes fun and deconstructs the design choices of metrovania games.

Two Brothers. The dialogue was just gibberish because it wasn't important at all, it was only supposed to show the player how the characters felt in different situations and their attitudes when they interacted with each other. All in all, this game was it's own thing and the players input was important in this story. It showed how just how powerful video games can be in telling stories.

Honorable mentions: 

-fez 

-Braid

-Thomas was alone (minimalistic, and the gameplay and story were intertwined with each other)

-The Lone Survivor (a side scrolling horror game that takes a lot of inspiration from Silent Hill 2 but it's still it's own thing)

-Guacamelee (a beat-em-up/metrovania game and the combat mechanics are used in platforming) 

-Proteus (sensory deprivation)

-Sound Shapes (A "musical" platformer with the best online community)

Risk of Rain is really fun especially when you play with others

Super Meat Boy is really excellent. A solid platformer, tight controls and extremely difficulty. Quite a bit of replay value too, you have the main light world levels and once you clear the par time on each it unlocks the respective dark world level. There's also an extra worlds and levels, other characters and user made levels. Quite a lot of content and highly recommended for 2D platforming fans.

Rogue Legacy is a rogue-like Metroidvania and everytime you die (which you will, it's a pretty difficult game), you start with a new character. However you get to keep your upgrades and the bosses stay dead, might get frustrating at times because of the randomness but overall it's a lot of good fun.

Still need to finish Cave Story and Shovel Knight but I've been having a blast with them.

Fez
Shadow Complex
Limbo
Guacamelee
Trials Evolution
Minecraft
Plants vs. Zombies