I will reiterate Monster, what a fantastic series.
If you don't mind a little blood and gore and gratuitous sex, Rin: Daughters of Mnemosyne is something I watched lately and can recommend. At least, I enjoyed it. It's a short OVA so it won't take you too long to finish if you want to.
A classic I enjoyed from back in the 90s, and probably one of my absolute favourites, is IRIA: Zeiram the Animation. An often-overlooked and very unique scifi classic.
You'll probably see a couple people in this thread recommend Black Lagoon. It's got about all the depth of a hollywood action flick but it's very polished and the fight scenes are well executed.
A friend of mine watched something a couple years back called Bartender, his review of it is here. I've still been meaning to check it out, but I keep forgetting. It looks pretty unique.
Right now I'm watching a fantasy anime called "The Beast Player Erin." Despite what the thumbnail suggests, this show is enjoyable for adults as well. It centers around the life of Erin, who lives in a village and takes care of giant lizards. A tragedy forces her to leave the village and the series follows her as she grows into an adult. Very involving and very well imagined, even if the beast lords look a bit silly.