Browser Games
Since there was a thread for mobile games, I thought I would start one for browser games.
Two that I have recently found and enjoyed are cursors.io and agar.io.
Feel free to add browser games you enjoy to the thread. Maybe we can start some discussion on them, or even play online together sometime.
In cursors.io your objective is simple, move your cursor to the green box on the screen.
They start off simple, like this maze.
But then you have to rely on the help of others...
This image shows the two ways you need other cursor's help:
1. The pink shaded box in the middle with the number 1 in it designates that one cursor needs to be in the pink zone to remove the pink roadblocks.
2. The colored and bordered boxes in the corners designate that they need to be clicked a certain number of times to remove those colored blocks. Once they get to 0, then the blocks are removed, but the numbers slowly increase so you have to be fast.
Many times in this game, you have to sacrifice yourself to get through and wait for another wave of cursors to get through the previous levels. Or you can be a dick and zip through without helping anyone.
Easily beatable in a half hour or so.
In agar.io (also a mobile game) you start as a small cell collecting food in an agar plate. In theory.
Gameplay wise, you are a blob collecting smaller blobs by following your mouse.
As you do, you get bigger. And slower.
If you are sufficiently larger than the other cells around you, you can swallow them up.
If you get big enough you can split into 2 equal smaller cells. You may want to do this to shoot out and swallow a smaller cell (make sure your half mass split will be big enough to swallow them though). You may want to split for added speed/mobility. Or you may want to split to escape from a bigger cell that is swallowing you... to at least live a little longer.
You can also extrude mass in front of you to help someone else get bigger, or to bait them to getting into your path.
There is a free-for-all game mode and I've been on a single server with 80+ cells roaming around. Only ever got to the top 5 leaderboard once in FFA, and I think it was a fluke.
There is also a team mode where you are assigned to one of three teams (green, blue, red) and there is a pie chart. Your teammates can't eat you, but you can extrude mass to them to help them get bigger to either consolidate team mass on a big guy, or to make the smaller ones less susceptible to getting eaten.
You can register an account and level up (larger starting mass).
In both modes there is no direct in game communication (but people have formed clans all over the world) and no consequence to dying... you just get to start over as a small little cell. I don't know if there is any winning at all, but there might be in team mode.
“Force has no place where there is need of skill." Herodotus
cursors.io felt like one of those psychology experiments to see if people will help each other or be greedy. It got to be a drag when you needed at least 5 cursors and no new players were coming along. I didn't finish.
agar.io, however, is awesome! Your instructions here are enough to get started (I didn't seen any official instructions on the site). Here's my best game so far:
I survived for an hour, was in the top ten for 45 minutes, and achieved first place for awhile. The green graph in the background shows your mass versus time. When you're a giant your biggest threats are viruses (the green circles with fuzzy edges). If you run into one it will split you up into little pieces. Get too close to a virus and another player can shoot it 7 times from the opposite side, causing a new virus to shoot out toward you with the same potential result.
Do you play as "Cheese"? I ran into a Cheese, which happened to be a cheddar orange color. 
It tried to eat me but wasn't large enough to succeed. My nickname is stabby.
Better than my best time/score!
I change my name on a whim... in team mode I go by "mini me" or "feed me seymour" depending on if i want to be a feeder or fed. The sad thing is that your score (and thus progression through levels tied to your name) is dependent on you largest size and time alive... so being a team player is rarely worth it from that perspective, but it's fun anyway.
In free-for-all i'll change my name to whatever the mood strikes or have no name at all. But I don't think i've ever been cheese.
I find the game most competitive when you're in the 100-400 mass range. Much bigger and you can slowly prod along and try to corner people (and watch out for viruses!), smaller and you're not worth the larger one's time to eat. You have to be careful not to be too close to others near a big guy or he can split and eat you all.
I decided to leave viruses out of my game intro to leave that discovery to the audience. 
One more thing. If you're smaller than 150, you can go right over/under the virus particles. For this reason I find it really useful to turn on the "show mass" in the options so that you know how big you are at all times.
“Force has no place where there is need of skill." Herodotus
After a one year hiatus I've tried to pick up agar.io again. It's practically unplayable now because it freezes up for a second or two at least once a minute. Also the lag is worse than ever. Try to run a zigzag and see how responsive the controls are.
I tried some of the suggestions to alleviate freezing but nothing has worked. Does it still play smoothly for you, Cheese?
I haven't tried in months (or more). I actually just deleted the app from my phone yesterday (it was never a good phone game anyway).
“Force has no place where there is need of skill." Herodotus