So lets say you make a really great game.
Do you think it will just “flow” out there like minecraft did? I mean, minecraft was the first of its type. Its not like it was a well made ‘clone’ of another game, yet many people picked it up.
Do you think that people just pick up good stuff and leave lame stuff alone?
The trick is to put it out to as many places as possible if it is good and you have a bit of luck the magic will work from there.
For example, if you post your game here and on many other forums and it is good and you follow your threads more than likely your game will find some fame.
What are you even asking? Minecraft wasn’t the first game of its type, nor was it the first to go indie famous, it was just the first to make millions upon millions and gain millions of players.
Yes, with no advertising.
Make a game people can play for a long while. They will share it, if they do it long enough. You can place a game everywhere, but possibly the people do not want to share it if they play it just a few ours.
With no advertising? That’s hard.
I believe Notch’s success came from the fact that people like to build and create. Sure, shooting games are fun, but only to a point. People like to build and share their successes, and Minecraft enabled gamers to do that. I find Minecraft more fun than say an FPS because there is an underlying sense of accomplishment when you complete a build, and on top of that I can keep that creation which let’s me remember. With an FPS you just kill, get a score and move onto the next round. If you do something awesome then you have a sense of accomplishment, but otherwise its just running around shooting.
You need to create a game that everyone can relate to. Anyone can relate to Minecraft. You can build, hunt, mine etc… All which are parts of everyday life in a way. If you want your game to blow up like Minecraft, first develop an amazing game and then advertise around a little. You cannot do it without at least posting your game on a few forums. Its just not possible.
You also need to let people have a hand in the creation of the game. Notch would take suggestions and actually imement them, would a big game dev company do that? Hell no. Again, its all about relations.
I wouldn’t say that “build and share” is the part that people like so much.
Its the overall score of the game. Minecraft is just awesome.
Take league of legends and dota 2 for example. Sure, league has lots of adverts, but all the friends I know that play league of legends started playing it, because their other friends were playing it. I remember the day like 4 or 3 years ago when my class mate told me about this game. I said I would give it a try. My brother saw it and said it was shit. After a while he started playing it too. Later, other friends joined in too.
As for dota, I used to play it with my friends a little bit. But it really got boring after few matches. Dota 2 came out, I tried it and quit after the first game. Sure, its a new polished game, but it had the same mechanics as dota from warcraft 3… I mean, it seems like they just redid the graphics and didn’t even bother to improve stuff…
For a game to be popular, it needs to be really good game, which you can play with your friends! 
I kind of have to disagree with your first sentence. Why? Well, look at legos. Millions of people love legos because you can unleash your creativity upon a bunch of cheap plastic shapes that can be re-used hundreds of times, and they are easy to work with! Just snap them together.
I think Minecraft was successful because of my above statements, and because it is easy to play (allowing for the younger crowd to share in the fun), it’s cheap and you can be creative and create crazy structures, blow them up and build them up again in any shape or form that you could with legos.
People never stop being kids. (Most of us) miss our childhood when it was simpler and you could play with awesome toys without getting weird looks. Society wants us to be big strong adults who don’t like toys, but inside we all do want to go back to the days when we were free and could pretty much do what we want. I think Minecraft brings back those memories via blocks. Blocks look like legos, you can build stuff with blocks. Not to mention all the other stuff you can do in Minecraft. It’s a unique game that pits you against a wilderness full of cute pixely structures and mobs that want to kill you. It’s fun, simply put. Some people might not agree, and that’s fine, but I think many people find surviving fun.
And then of course you have the social pressure to try the game out and play with your friends, and like you said people love being with other people. It’s how we are supposed to be, we are created to be social. So playing games with your friends and sharing those awesome experiences? Who would pass that up?
Word of mouth will always be more effective than advertising.
What hahaha?
Other than that, your probably right. Minecraft’s claim to fame was playing off the users desire to build.
Minecraft may have had alot of community support, but its not like they support modding or anything.
I said in a way 
I don’t mean we literally mine.
That’s not fair to say. They fully support modding obviously, there are thousands of mods out there. Sure, they don’t “officially” support it, but they are working on a mod API. The game has survived thus far pretty much because of support of mods, however.
Please, do not let this become a pure what-Mojang-does discussion ok?
Minecraft might be is a super-famous game and probably very ‘good’ (my favourite word ‘definition’ again), but not mainly because of its developers but of itself.
And even though it is maybe the best example for a massively growing indie game, there are also enough other ones.
Lottery Success.
If you make a great game, you win. If you make a not so great game, you win less. Its probably that simple in the internet connected world.
I imagine it’s a mix of word-of-mouth, a quality product, unique elements (or just well re-imagined elements) and some luck.
Really though, I think a fun to play, well polished quality product will “sell itself” as long as you can get at least a hundred~ people playing it. A good example is Tim Spekle’s FarSky. I think he’s going to be one of the guys who actually make some serious cash off his product. It’s already on it’s way to being greenlit on steam and make some money. (he has over 6k votes last I checked) Why? Because it’s a unqiue spin on a concept everyone loves, and it looks like a quality well polished product.
(here it is on steam http://steamcommunity.com/sharedfiles/filedetails/?id=226898710&searchtext=FarSky )
I wont call any bad games out, that’s just rude, but we all know what games in the WIP/Showcase that are not going to “sell”, a lot of people see their own products with rose-glasses, so they can’t figure out why they can’t sell their games. 
Sorry; I don’t mean to sound cynical/pessimistic, Just trying to give realistic and candid input.
Minecraft, Flappy Birds, World of Warcraft?
Yeah, I think it has to be the networking and how long people actually leave the game on their device. I get a lot of games through word of mouth, but you still need to generate followers. I think the missing element many people forget is the fact that a game has to be fun (either in challenge, interactivity, and/or socializing) in order to maintain the retention rate to spread. Having an easy to remember title helps too.
Farsky is very interesting because it hasn’t been done. Underwater first person exploration and survival is just new and better than the hordes of zombie games out there. It’s a refreshing change of pace. The last time I’ve been excited about an underwater game was Echo the Dolphin… I can’t believe I just said that lol…
I don’t understand how flappy bird became so popular. A lot of it was obviously word of mouth, but why did people keep playing it? Do people like games where you can’t win, or it just makes you frustrated? No, they don’t. And yet, flappy bird was still a huge success. I think that people just like change. Make a game that is original and has the feeling of “just 5 more minutes.” Then, put your game on forums like indiedb, desura, and tigsource. Go for something like a kickstarter or steam greenlight. Advertising is a major aspect of game popularity, because if you have a wonderful game but nobody knows about it, then it is not going to become popular. Also, hype may be a factor. Like instead of just releasing your game, advertise before you release it. I will probably attract a lot more people.
Because it’s challenging and the input is easy, everyone can play it.
The name is great, if you search for angry birds you also founbd flappy birds. The graphics reminds of mario and look cute.
The game was made for it’s plattform, that’s what a lot of developers do wrong. You won’t be successfull with a game that’s not made for the input device. For example FPS and strategiegames for WII :
The way I look at it, even horrible advertising can sell well but I’ve seen more than my fair share of amazing games with poor advertising that don’t sell at all… I’d rather ere on the safe side
More than 1300 persons per month tested TUER in 2008 whereas its graphics aren’t good and its gameplay very limited. I agree with The Lion King. The people can talk about a game even though they only play a few minutes with it.