I think browser games are getting phased out by mobile gaming, but I do enjoy having something to play while I'm working on my computer. One of my favorites is Kingdom of Loathing, especially since I can not play for a year and just hop back on and have some fun! Kongregate is one of my most visited sites, and I get sucked into "clicker" games way too easily. >_>
I sometimes play Browser games when I am bored, and I am login to Facebook, Miniclips, and similar sites which has a lot of browser games to play on its site.
I think browser games have become less popular because of mobile games, but people who are at school and work are sometimes not allowed to use their smartphone for non-work or non-school related things. But, with browser games, you can play a game in a separate tab, or window while your teacher or boss is not watching you. When you hear someone coming toward you, you can quickly switch to another tab, or program like MS Word, and start working again.
I used to play browser based games all the times in my youth because that is the only real option you had for school computers and even at home since I was young and couldn't afford to buy myself a decent gaming PC. Ever since the day I got my first gaming computer I essentially completely stopped playing all of them however. I'll still hop by an old browser game for a brief bit of nostalgia from time to time, but never as something I actually play all day or consistently.
I've been wanting to find some good browser MMOs that can match the downloadable ones but I haven't found any that I like nearly as much yet. The browser games that I usually play are on Facebook and they're your typical casual games but they don't usually hold my attention for long. One that I've played for a few years now though is City Girl Life. I go through phases where I play it all the time since there's always new limited time events on there and I'm a big sucker for those. It reminds me a lot of The Sims. You have to keep up your character's happiness, energy, hunger, ect, and they have a career and everything.
I play the r.io games, and I'll search up the classics and play those, sometimes even the breakout easter egg on google. Browser games will always have a place when other games require finding a disc, a time commitment, or even a boot-up time on the game or console. It's just a spur of the moment thing, but it'll be really fun in a few years when almost every game is a browser game, a man can dream.
I play Kingdom of Loathing! It's always good for a laugh with the text and the drawings and the special challenge paths have made the typical runs very exciting as a whole. It's been going on for so long, but I do like that they're trying to rebalance the game (by locking items/familiars over two years old in current challenge path/standard runs).
I used to play other browser games like Fallen London, Twilight Heroes (which I do still check from time to time), but the first website that really got me into it was Neopets as a kid. Oh, Neopets. It's changed so much from what it was before (and not for the better).
With the shift of casual gamers to mobile as a whole, it makes sense for browser games to adapt and at least give mobile apps/mobile view (to compensate for smaller screens, etc.). KOL at least is trying with their mobile view, though of course there's still room for improvement.
I play Manyland sometimes. It's basically a "sandbox" 2d game about building things. You have to either draw or copy items drawn by other members. It's all user-made, which is amazing. I think it's not fully completed though, which makes it lag a lot. But I'd suggest it to anyone who likes creativity games...
Man, I remember the days when Browser games was the jam. I even started collecting them online to place on a site of my own so I could always have access to my favorite titles. Most of them were even playable from the browser of the sony consoles when you got online. But I can see why this would become a thing of the past with the app market. But it isn't like that in every part of the world.
I remember playing Kingdom of loathing a lot several years ago. Is highly addictive, and simple to get into. You create your character on the main page, choosing which class you want to be, from there, you just activate your account and can play. You get forty adventures a day (there are ways to get more) that you can use doing whatever you want, some things require adventures, and some don't. Adventuring allows you to go to areas and either explore them or fight monsters, getting stats that allow you to level, items that can be used to boost your characters power, or be used in your characters crafts and meat (the in game currency). Pretty silly but is really a good time sinker when there is nothing else you can play soon.
Have you ever tried Begone? Its on a website called Nplay, and it is a fairly popular shooter that is pretty smooth and considering you don't download it, it does incredibly well. Alot of people I know play it because they don't have space to download other bigger games. You can also try out Town of Salem, it's about the town of salem(duh) and it is an incredibly complicated puzzle game.