Game development can be a very lucrative occupation with room for people of various talents. There is room in the field for programmers, artists, sound designers, and even though it is frowned upon, there is even a little bit of room for "idea guys" (and gals too, of course). Many of us (including myself) grew up playing games and thought to ourselves how cool it would be to make them!
Of course, back in those days (I'm talking ten to twenty years ago), most of the games that we played probably came from big companies. This still holds true, but indie games are becoming more prevalent, sometimes rivaling the quality and fun of games by big-name producers. Nowadays, it's easy for someone to pick up some free developing tools and put together games from the comfort of their own bedrooms, making the dream more tangible than ever. This also means that there are millions of games that can be found on line, some of them gems, but many of them heaping piles of poorly made mess.
I have been playing Flash games since 2002, and making them since 2006. I have seen the medium evolve over time, and it is arguable that I have seen its apex and the beginning of its decline. Some of the games that made front page on Newgrounds back in 2005 would probably only earn a 2.5 average score these days, and be forgotten amongst the masses of other games as players have begun expecting amazing graphics, pop-up instructions, and a bit of casual or hipster humor. The advent of mobile devices, some of which are not compatible with Flash at all, as well as HTML 5 and Unity have also lead to a slight decline in Flash gaming's popularity.
Not all indie games are Web games either. As stated in the previous paragraph, games for smartphones, such as the Android and iPhone, have become quite popular. There are also a litany of indie games developed for computers themselves, some of them good enough to appear on Steam. I've never paid for one, though this is not out of discrimination; some of the indie games look downright fun and remind me of the DOS games that I cherished as a kid. I don't pay because many of the indie games that I like are free, such as Naev, an Escape Velocity clone, and Wing Commander: Standoff, a standalone mod for Wing Commander Prophecy: Secret Ops.
With the bar raised so high for indie games these days, it will be hard for average "hobbyist" designers to break into the market. It is still possible to make a bit of money from it though, and I speak from experience. I've never created a viral game, and probably never will; I have, however, made a bit of money on the side creating advertisement games and games for small educational websites.