I'd have to say that Newgrounds.com's success is based on a multitude of things, some of which I'll mention, most I won't, because it would take longer then I have the patience for.
User Based Content
Most sites out there that are even comparable to Newgrounds in size, have a limited, or no actual system to upload new Flash to the site. Anyone can come to NG and upload a movie or game. Try doing that at sites that are as large as NG, and legitimate.
Free Use
Larger sites, especially ones made by corporations, usually ask for a membership fee. Anyone out there can come to NG and showcase their work, or join the community.
Originality
First, or I should say, one of the first portal systems on the internet. It's not really quite clear whether NG was THE first Flash Portal out there, but it is, without a doubt, the oldest now at least.
BBS
Let's face it, anyone who is familiar with BBS's knows that 90% of the web uses the same damn thing, just different "themes". Everyone has seen a BBS at some point, that has pointless Forums, no limits on Sig size, and no limits on Font size. Fucking pathetic. I'm personally fucking tired of seeing PHPBB, or Nuke, etc, etc systems everywhere I go. It's even sadder when large businesses use it for their site. NG's BBS is clean, well thought out, one of a kind, and organized. It's basically a sort of glue for the site to, it keeps people connected, and gives a part of the site, anyone can participate in, regardless of flash skills.
Homegrown
"No, it wasn't made by some giant company - just some dumb kid." - Tom
Let's face it, corporate sites like Atom Films cater to what's popular, they only care about money, and don't give two shit's about actual content. NG has such a wide spectrum of content, from some of the biggest rising stars in the flash community, to some of the worst. I know I enjoy all of them, whether I'm laughing because a stick movie is so horrible it's actually humorous, or whether it's shit that deserves to be on Adult Swim on CN.
Games
Birthplace to Alien Hominid, Pico, and thousands of free games that are a notch above the rest. There is literally something from every genre of gaming here, that's always available to anyone.
That's what makes NG so successful.