Reposting my own comment from the last time this thread happened:

This is my personal list of the best Flash games of the last 10 years or so. For many of these, the entire series makes the list, but I'm just listing the best game here. I am excluding Point N' Click games because I don't enjoy them. So without further ado:

-Grey Matter This is an "antishooter". It's an incredibly unique take on the Shmup genre not for the faint of heart.
-Don't Look Back From Terry Cavanagh, the creator of VVVVVVV and Super Hexagon, this game is a simple 2D platformer/shooter that retells the story of Orpheus. What makes this game great is not the gameplay persay, but rather the way it uses gameplay to tell a story. AAA designers should take note of games like this.
-Z-Rox is a one dimensional puzzle game. As bizarre as that may sound, this game really pulls it off. You will find yourself boggled by how amazingly challenging one dimension can be.
-Tr-Achnid is a journey. It's crazy and alien, but it is totally unique. Some may find problems with the pacing of the game, but I think the unique control scheme and well designed puzzles more than make up for it. One of Edmund's early games.
-Amorphous+ - Built on a simple mechanic, Amorphous+ finds ways to bring incredible depth to it. This top down hack n' slash game is highly immersive and has hours of gameplay.
-Spewer is a puzzle game based on throwing up. That should make most of Reddit fall in love with it right away. The puzzles are great, the diversity of vomit types keep the game interesting, and the sound effects and level design are top notch. Oh, and it's made by Edmund. If you like the Edmund games I listed here, you can buy them in The Basement Collection on steam to support him and get some extra goodies.
-Super Mario 63 - This fangame manages to capture a lot of the best parts of Super Mario 64 and Super Mario Sunshine in a 2D demake. It has a few minor glitches, but you will feel like a kid playing Super Mario 64 again the whole time you are playing. That alone is worth it in my opinion. This is literally the best mario fangame I've ever seen. (Oh, and it has a level editor for infinite content.)
-The Space Game is a hybrid of mining games, tower defenses, and real time strategy games. It manages to hit all of the high notes of all three genres. It's perfectly crafted to have simple gameplay that applies to tons of different situations and keeps your strategy bones tingling the whole time. If you want more, The Space Game: Missions is an expansion pack.
-Portal: The Flash Version - Originally debuting just before the first Portal game came out, this game managed to capture the core puzzle mechanics into a beautifully coded 2D puzzler. It lacks the humor aspect of portal, but the puzzles and strategy are completely intact. This should be the first stop for anyone who is a fan of the Portal series and of Flash games.
-Aura Braver - This Shmup is one of the more unique choices on my list. It was originally ignored upon it's first release and seen by only a few thousand people. I found it amongst one of the Hidden Treasure competitions on Newgrounds along with about 100,000 others. The core mechanic of this game is just so fun to play around with and makes the gameplay different every game. This may not have the level of content of other games on this list, but it is easily worthy of more notice than it has gotten for it's polish and fun.
-Level Up! - Level Up! is a hybrid of RPG and Metroidvania genres. This game is so fun to play and has such a great mechanic that I replay it every few months. It's a 2D platformer in which you level up and learn new abilities by doing them and gaining experience for that skill. (For example, jumping a lot levels up your jumping and lets you jump higher.) One of my all time favorite games.
-Hero's Arms is a blatant Legend of Zelda rip off. Yet even so, it's the best I've seen in that genre. It feels very much like playing the original LoZ condensed into a short Flash format. A great way to spend an afternoon.
-Wrath of Anubis is a hardcore puzzle platformer. It's a bit like Super Meat Boy, but with physics that are much less slippery. I love to speedrun this game and try to optimize my routes through it. Anyone who is a fan of the Platform Hell genre should give this game and/or it's sequels a try.
-Robot Wants Kitty is a simple Metroidvania and the first in a series of multiple games. The mechanics are simple and the objective is simple, but it's rare to find well implemented Metroidvanias anywhere. The later games really carved out a niche for themselves with unique mechanics, fun puzzles, and awesome level designs. I choose to start here however, at the series humble beginnings.
-Super Mario Bros. Crossover is a fangame that recreates the original 2D Mario experience and level design perfectly. But then it adds all of your favorite 8-bit and 16-bit characters to the mix to create gameplay that you have to experience to understand. If you've ever wanted to shoot Goombas as Samus, this game is for you. In addition, the creator has started a kickstarter to make his own game in the same style with characters that aren't copyright. If you enjoy the game, you can learn more about his new game or donate here.
-Motherload - It's been said before and it will probably be said again. This game is amazing. Motherload recreated the mining game genre and stole dozens of hours from unsuspecting children and teenagers across the planet. This is a core experience for every Flash gamer and shouldn't be missed. They are now working on a sequel for Steam. Super Motherload has been greenlit and will come out after they release it on PS4. steam greenlight page here.
-intrusion is the single best 2D shooter on the internet. It has a ragdoll physics system that is incredibly fun and great gameplay mechanics and enemy encounters built around it that will keep you riveted to your seat from the moment you start playing until the end. There is a sequel on Steam if you enjoy the game as much as I did.
-No Time to Explain is a zany and fun short platformer. It's about time travel, lasers, dinosaurs, and much moar. There's no time to explain more about it, just go play quickly! (You can find a sequel on steam here: http://store.steampowered.com/app/227280)
-Rebuild 2 - This is a zombie survival strategy game. It drops you in a randomly created world tasked to survive long enough to find a cure or die trying. I lost days to this game trying to find the optimal way to win with each of the possible victory conditions. It's simply one of the best flash strategy games out there.
-William and Sly 2 is the most beautiful Flash game I've ever played. The graphics will awe you constantly as you search for pages to unravel a mystery. The pacing is calm and laid back and nothing ever rushes or hurries you. If you want a chill afternoon of gaming, look no further.
-Snailiad - This Metroidvania has a great design, awesome power-ups, great humor, and inspiring level design. If you are a fan of the Metroidvania genre, you can't miss this game. I mean come on, it's a game about Snails!

Edit: Fixed mistakes that users pointed out and corrected broken links. Thanks!