I bought the game when it first came out (2003? Boxed, from Target) and played with an online friend for a while. We mostly mined and we didn't really have a corporation, it was just the two of us. There wasn't much else to do at the time. At one point I fell asleep at my keyboard during a mining op. Gave up soon after.
In 2015 a coworker talked me into trying it again. We joined a small corporation, swore fealty to a larger corp (Brave? Band of Brothers?) and moved to low-security space. We got involved in massive 3000+ ship battles, some of which made the news. These are not as fun as you would think.
However, the most fun I had was joining 100+ ship bomber fleets that would warp in on unsuspecting mining operations and destroying billions of ISK (in game currency) worth of ships. We'd use Mumble for voice chat, which allows for a hierarchy of chat rooms, so that we could hear the fleet commander giving orders but he couldn't hear us. It was super organized and our fleet commander was really skilled.
In the end I couldn't keep up with the time commitments. For the fun stuff, you had to be online at a certain time and there was a lot of prep involved (buying the proper ships which changed all the time, getting your ships to the right station, etc). I still consider it some of the best multiplayer experiences I've ever had though. Nothing beats warping in and seeing those huge mining ships and then hearing the fleet commander start issuing targeting orders. It would raise the hair on my arms.