Sword Art online, though a season 2 is in the making.
Buddy Complex, same as above. Neither have cliff hangers at the end.
Soul eater.
Code geass
Guilty Crown
Shaman King
Mobile Suit Gundam Seed & Seed Destiny, Fullmetal Alchemist Brotherhood, Samurai X, K anime, Inuyasha & etc...
Samurai X, didn't forget this word "Battousai The Slasher"
Mobile Suit Gundam Seed/Destiny, "Freedom" & "Strike Freedom"
Dragon Ball, "Saiyan"
K anime, "King"
Another is a great anime (sorta thriller/horror on a school).
About 25 episodes or so.
Go check it out.
I looked up a few more for you.
Anohana is about 13 episodes (funny and emotionally touching, about a girl named Menma, who is a ghost. Her friend can see her. He and his friends try to find a way for her to rest in peace).
Sword Art Online.
About MMORPG's.
The main characters meet in an MMORPG and eventually fall in love.
Dying in the game can mean dying in real life.
I dont remember the amount of episodes, 25 or 50 maybe, but it is a finished storyline too.
I would definitely recommend Code Geass.
Death Note is also awesome.
Another is also worth watching, why not some gore. XD.
Sword Art Online
Guilty Crown
Ao no Exorcist
I would also recommend an ongoing anime No game, no life
And if you want some extra comedy there's Noragami. (Manga is good too.)