Newgrounds is, I believe, the first website to open a flash portal where just anyone could submit their movies and games. If not, it was among the very first few. This made it hugely pivotal to the development of movies and games in the early 2000s era (I frequented the site at that point in time, but did not have an account or upload any work). This gave it a much larger sense of community, as the users were the artists, and vice versa. The members of the site were a lot closer than those on, say, StickPage.com or ArmorGames.com, where the artists seemed like strangers behind another screen rather than people you know. As well, Newgrounds always had a more genuine, honest personality, whereas sites like Miniclip.com or AddictingGames.com, again, as much as I liked them, seemed to be more inclined to playing it safe and adopting a generic, kid-friendly model. This enabled smaller or newer artists to take more risks in a community that was supportive of 'unpolished' productions, so to speak. I don't want to make it sound like the work here wasn't good - not by far, we have seen some amazing talent over the years - merely that artists were free to not be perfect as they "sewed their wild oats" and grew.
The age of flash is drawing to a close, however, and it seems it will likely be completely out of style within the next ten years or so. This site hasn't really been relevant for quite a few years, and I don't foresee it ever having the same relevance among other sites that it once did. It's a shame, it seems my highest level of involvement with the site - becoming a member, getting to know the community and being a part of it - was on it's way out. Many of the old regulars and artists are gone - some leaving for bigger projects whose revenue could better support them, some losing interest in the site and its community, some losing interest in flash altogether, some dead, and some simply fading into the unknown.
However, the personality of the site, it's genuine sincerity and lack of political correctness or commercialism, still allow it to stand out from others. Some of the old users are still here, and it's nice to see them from time to time. Some of the old artists are still submitting their work, and it's nice to see what they're up to. Above all, it's important in my opinion to remember how imporant this site was, and arguably still is, to young and aspiring flash artists.
In regards to my own personal experience, as I said, I frequented the site when I was younger.
I came back around 2008, when I was 13, and saw that it was still interesting and had a lot going on. I signed up and fell in love with the content and the community. As others like yurgenburgen have said, it appealed to my angsty teenage mindset, and it just seemed like a fun way to escape for a little while. I've been less active these past couple of years, but I still get on every one and a while to see how things are doing.
Feel free to respond or PM me if you have any further questions.