Going to note that the following doesn't really "copy" haven, just is similar in many aspects such as the "openess" and crafting.
One that hasn't been mentioned this time (that I recall in this thread), but I've mentioned it in the past, is what you'd have if you took the combat out of Haven:
http://www.atitd.com/ The primary goal is socialization and the progression of civilization through cooperation and competition. Lots of art projects for those that like such things, leadership contests (who knows the other players better, or can actually get into positions of power), building massive structures such as pyramids and temples, and the more "scientific" pursuits of crafting food, booze, and cataloging plants.
Even for running for 15 years and a smallish player base (about the size of Havens), it's still a great game. The only downside is the $15 a month. The previous developer did take bitcoin, though I'm unsure if that is still an option. Several of the players finally convinced Teppy (short for his Egyptian name and original designer and developer) to let some of the more talented players that had development experience to take over the game while he pursued other projects.
I haven't played in a few years as I haven't had the money to maintain a subscription, but I've been in love with it ever since my brother told me about it not long after it opened up.
Opinions expressed in this statement are the authors alone and in no way reflect on the game development values of the actual developers.