1.) Black Cat - Without a doubt, my favorite manga series. It's largely unheard of, and in my opinion, severely underappreciated. The series was finished recently, and now it's been licensed. I definitely recommend at least browsing a copy if you find one. It's an action series about bounty hunters. There's an anime series in the works, and I'm very excited to see it.
2.) +Anima - Another underappreciated series. The artwork is lovely, and the story is incredibly cute. It's a sort of fantasy series about kids who have certain animal abilities like flight or strength. So cute. ^.^ There is no anime series for this, but I wish there was. It would be so cute. The artwork is pretty detailed though, and an anime series would probably ruin some of the charm.
Edit: Turns out +Anima has been licensed by TokyoPop. So read it if you get the chance. ^_-
3.) W-Juliet - While I don't usually go in for romance, this is one of the best series I've read. It might be the drama lover in me, since the background is about a group of drama kids. Funny, charming, and one of the best romances I've ever read. No anime series of this either, although I have a fake one in my head with Saiga Mitsuki and Ishida Akira playing the lead roles. If they do make a series and they don't cast these people, I'll probably be a little disappointed, but happy anyway. XD W-Juliet has been licensed, and I've seen some of it in stores. Check it out if you get the chance.
4.) Spiral ~ Suiri no Kizuna - One of the best mystery manga series that I've ever read. The characters are deep and well thought-out, the story is fast paced, and the mind games really make your head spin. There is an anime series that has been licensed by Funimation. The entire season has been released, so watch if it you get the chance. The anime does not cover the entire manga series however, so if you want to know how it ends, you'll have to read the manga (licensed by TokyoPop).
5.) Partner - This is one of the creepiest things I've ever read. Ever. While it's not quite mess with your head crazy like Paranoia Agent or Lain, it's definitely a trip. The art style makes it especially creepy, since it looks like your typical cute shoujo manga, but it's drastically different. No anime of this either, although I think it would make an excellent anime. It hasn't been licensed, but you can find scanslations online.
And those are my top five manga, in about that order. I really like a lot of the things listed here like Yu Yu Hakusho, DNAngel, Bleach, Azumanga, Death Note, and D.Grayman, but I figured I'd list some more obscure ones to spread the love. ^-^