I looked through Paul Gravett's list of 1001 Comics You Must Read Before You Die to see how many of them I've actually read.

2008: Freak Angels 
2004: Astonishing X-Men I dropped it after chapter 7
2003: Death Note previews in Shonen Jump and the Death Note Black re-release
2003: The Walking Dead read the first two albums
2001: Bleach in Shonen Jump
2001: Fullmetal Alchemist 
2000: Chobits
2000: Cromartie High School
2000: Honey & Clover Shojo Beat
1999: Fruits Basket my Sister gave me a set for X-mas
1999: Nana Shojo Beat
1999: Naruto Shonen Jump
1997: One Piece Shonen Jump
1996: Kingdom Come 
1996: Yu Gi Oh! Shonen Jump
1995: Neon Genesis Evangelion 
1994: Blade Of The Immortal
1994: Tekkon Kinkreet: Black & White Pulp
1993: Ghost World Eight Ball
1993: Sin City (That Yellow Bastard and A Dame to Kill For)
1991: Bone a single issue (can't remember which)
1991: Weapon X a few of the closing chapters in Marvel Comics Presents
1990: Shade The Changing Man
1990: The Last American
1989: From Hell
1989: Ghost In The Shell
1989: Sandman
1988: Tank Girl
1986: Batman: The Dark Knight Returns
1986: Five Star Stories I've only been able to find the first collection (of two chapters) at a reasonable price
1985: Banana Fish Pulp
1984: Dragon Ball
1984: XIII: The Day Of The Black Sun
1982: Akira
1982: V For Vendetta
1978: Garfield a few strips from syndication
1977: X-Men: The Phoenix Saga
1976: From Eroica With Love CMX preview
1976: Swan
1972: Buddha
1970: Green Lantern / Green Arrow I bought a few copies for a quid at a Toy Fair a few years back
1970: Lone Wolf & Cub
1970: Ode To Kirihito Vertical Preview
1970: Red Colored Elegy Vertical Preview
1965: Asterix In Britain Library
1963: Amazing Spider-Man Mighty World of Marvel reprint
1963: Avengers Mighty World of Marvel reprint
1963: Dr. Strange Essential collection
1962: Incredible Hulk Mighty World of Marvel reprint
1961: Fantastic Four Mighty World of Marvel reprint
1959: Tintin: Tintin In Tibet Library
1951: Dennis The Menace (UK)
1950: Dan Dare my father read this as a child
1950: Peanuts collection of early strips when Snoopy was still dog-shaped
1943: Tintin: The Seven Crystal Balls Library
1942: Tintin: The Secret Of The Unicorn Library
1939: Batman various reprints
1938: Superman reprint of first story
1937: Desperate Dan
1936: The Phantom reprints