Hmm, well there's Mushi-shi (each episode is pretty much a self contained plot so it ends very well, it also has a second season in production now)
Black Lagoon: the manga is still going on, but by the end of the OVA "Roberta's Blood Trail" it feels pretty conclusive, making it a good jump-in point for the manga or a good ending point if reading isn't your fancy.
Berserk: This is one of my personal favorites, and it's not one of those anime you hear about outside of specific circles otaku. There's the anime and the series of movies, both of which cover the Golden Age Arc of the manga (the backstory arc.) Sadly, neither end...period. The mangaka has been writing it since the late 80s and there's no sign of it ending any time soon, so you may want to avoid this. However, as with BL, the movies/anime are a great way to jump into the manga. It's an extremely messed up story that even makes Hellsing look tame, so if you can't stomach horrible things that I can't even mention on this board you may want to reconsider.
I hope some of these are new to you. Good luck