I owe my closest friendships and even my career to EVE. I'll expand on this in a bit.
While I did spend a few years floundering around in the game like most players do, I was lucky enough to get close to the major political action early on when the first alliance I was a part of, ISS, collapsed. The ties and relationships that I built here got me in-system to watch the first (BoB) Titan kill with my own eyes.
A few years later when wormhole space opened up, I jumped on that immediately and got involved with a corporation dedicated to taking advantage of the new resources and PvP opportunities. Within a few months I was an officer in the corporation and we had brought in some local blues doing manufacturing in a merger. I had a pretty good relationship with these guys; a group of three students from Denmark.
It became clear to me right away that my corp's CEO plan here was to screw these guys over and steal all of their assets, as well as the rest of the assets of the corp and do a runner. Without cluing him in, I managed to help everyone in my corporation secure their assets and he got away with nothing but the corp's wallet, which I made an effort to drain (spread out to members) and left only about 8bil ISK.
Immediately after, these students and I joined one of the most well known RP/lowsec PvP corps in the history of EVE and started our own manufacturing corporation on the side which turned into somewhat of a mini-empire. The students were programmers and I now had a practical use for a life-long hobby(but not really the inclination or skills to do professionally at the time).
One of them is probably my closest friend today. We routinely discuss the idea of one of us relocating and starting a real business together.
Other friends that I made in this corporation I still talk to on a daily basis...even after a few years away from EVE. Eventually our CEO had to shutter the corporation, as he took a job with CCP; most of us were getting older and finding it hard to find time for the game anyway and quit, myself included.
My account still has a few hundred billion ISK sitting in its wallet. I resist the urge to pop in and get deep into the game again, but it's frequently there. I've had some breathtakingly beautiful moments and experiences with people in my life because of this crazy game.
I'd done just about everything you could do in the game while I was playing it and had about 4 accounts at any given time. A lot of quitting players complain about not being able to find the real action in the game...while it's hard, everyone who can read the forums can find out who the important, active corporations are in game. Seek them out, be available and make friends and then make enemies.