Having long-term goals in a game is one of the features that keeps me playing for more than a trial. In EVE I've had a number of goals since I started playing.
-Solo PVP (win or lose) at least once in every combat capable ship in EVE (and many that are not so capable). I talked about my progress in this back here and I should update soon about it.
-Get experience with every general form of PVP in EVE
-Get at least one kill in every low sec constellation in EVE
Exploration and General Gameplay
-Visit/explore every system in EVE at least once
-On my market and trading character, get to a full set of orders (304) and at least 50b in stable sell orders. That's what I currently count as “finishing” my market, but I am not sure what goals I have after that, including what I will do with (where/how I will invest or use) the extra isk. I have no goals for how much isk I'd like to have, for instance. Anything above a plex and some PVP ships a month is counted as extra.
It is cool to see other players with similar completionist type goals. Katie Sae at To Boldly Go is in the process of visiting every system in EVE, giving them a much more detailed look than I will / usually do. EVE Travel is another popular site that has encouraged me to visit the unique places spread throughout the galaxy.
I realized how worthwhile this would be even as a brand new character. Partly in virtue of the different graphics and ambiance of each region, certain areas of space just had a "flavor" to me. I started the game around the Verge Vendor area, and specifically around Luse for some reason. It had a certain feel to it, one that still brings back nostalgic memories. Clellinon seemed incredibly busy, and Dodixie seemed like it was on the other side of the galaxy, and the sisters of eve arc seemed like it sent me on virtual day trips around the EVE universe.
EVE still has that sense of scale to me, but one much more determined by the players who live in those regions than anything else. Heading into Khanid low sec, Surely You're Joking is everywhere and even the shuttles have cynos. Covryn in Placid is a place I started solo PVPing and continue to stop in occasionally, but it is ingrained in my thought as the(/a) home of Cynosural Field Theory, where you might die to a alliance tournament ship at any moment. Over the past year I've been spending time in every region, trying to accomplish some of the above goals (like getting a kill in every low sec constellation) and I might someday write overviews on different regions. Most of it is common knowledge for those who have PVPed long enough, but when I was starting out I had no idea how the PVP would differ in Genesis as opposed to Black Rise etc. Spending time in these regions has also taught me how frequently they change based on who lives where--and PVP corps don't generally seem to last all that long. This makes for a sometimes very rapidly changing game world, in a way that no other MMO matches so far as I've seen.