Gotta warn you about Claymore being a bit of a clunker when you get to the middle of the series, felt like the mangeka had too many ideas and couldn't pick where to take it.
DX, that is very sweet of you, thanks for your kind words. Unfortunately I used to watch a lot more a few years ago than I do today because of the nature of today's anime and it's primarily the reason why Attack On Titan grew in popularity. The past few years anime has had a lot of loli, cute, lets eat cake, upskirt, jiggling boobs, wind up your skirt kinda cutesy high school drama, comedy, slice of life, harem kinda stuff. Here comes Attack On Titan about killing and killing someone's mother or eating them and it came as a shock to the cake eating otaku who was expecting to see some speed lines of women in tight costumes or short skirts fighting demons/ monsters. Unfortunately, the series they all gripped on is not good where it truly matters - the meat of the story/ characters.
It's been a long time since I watched anything that grabbed me as much. From on-going manga I truly value or treasure, I'd say there's Berserk, Vagabond, Real, One Piece - amazing story telling combined with talent in the craft of the art of drawing manga and more importantly, depth in characters, them evolving or devolving and the story overall. Each of those are so different from one another and invoke different emotions as I read them. There are a lot of other completed series that I could recommend you read - Akira, 20th Century Boys, Lone Wolf & Cub, NANA, Barefoot Gen, Slam Dunk, Monster, Neon Genesis Evangelion, Jojo's Bizarre Adventure, GTO and a couple more. If it's anime you're asking about, there are a few I like in no order, including series or movies at the top of my head - Akira, Crest Of Stars, Banner Of Stars 2, Kurogane Communication, Planetes, Harlock Endless Odyssey, Robotech, Kurau, Fruits Basket, Twin Spica, Gankutsuou, Girl Who Lept Through Time, Angel's Egg, Hunter x Hunter, Kino's Journey, Boogiepop Phantom, Last Exile, Tokyo Magnitude, Macross Frontier/ Plus, Nadia, Saikano, Ouran, GTO, Perfect Blue, Millenium Actress, Blue Seed, Haibane Renmei, Place Promised In Our Early Days, Irresponsible Captain Tylor, Rahxephon, Escaflowne, His & Her Circumstances, GITS Stand Alone, Ippo original series, Voices of a Distant Star, Patlabor OVA, Gundam - Char and MS 8th, Paranoia Agent, Legend Of The Galactic Heroes, Battle Programmer Shirase ... there are a few more but I'll have to go through my stuff to dig and tell.