It would best to do 2 lists, one for UK Indie and the other for US Indie/Alternative:
UK:
Arctic Monkeys - Whatever People Say I Am, That's what I'm Not (2006)
Badly drawn boy - the hour of the bewilderbeast (2000)/Bob -Leave the straight life behind (1991)/ Brilliant Corners - somebody up there likes me (1988 - all essential)
Cud - When in Rome, kill me (1989)
Dr Phibes and the house of wax equation - Hazy Lazy Hologram (1991)
Eat - sell me a God (1989)
Fatima Mansions - Viva Dead Ponies (1990)
Gallon Drunk - Tonight's the night (1991)
Half Man Half Biscuit - Back In The D.H.S.S (1987)/Happy Mondays - Bummed (1988) - (both excellent)
I Am Kloot - Natural History (2001)
James - strip-mine (1988)/Julian Cope – Droolian (1990) - (both excellent)
Kingmaker – Eat yourself whole (1991)
Lloyd Cole and the commotions - Rattlesnakes (1984)
My Bloody Valentine - ecstasy and wine (1989)
New Order - Substance (1987)
Oasis - Definitely maybe (1994)
Pop will eat itself - This Is The Day--- This Is The Hour--- This Is This (1989)
Q?????
Radiohead - O.K. Computer (1997)
Stone Roses - Stone Roses (1989)
Tindersticks - Tindersticks (1993)/The Stairs - Mexican R'n B (1992) - (again, can’t decide)
U2 - October (1981)
Vaselines - all the stuff and more (1992)
Wonderstuff - Hup (1989)
XTC - Skylarkin' (1986)
You say party! we say die! - Hit the floor (2005)
Zutons - who killed the Zutons (2004)
USA:
Adam green - friends of mine ('Bluebirds' has the best rhyming of any song) - (2003)
Beck - Odelay (1996)/ Brian Jonestown massacre - Thank God for mental illness! (1996) - (check out both)
Cat Power - Moon Pix (1998)
Devandra Banhart - Nino Rojo (2004)
Elliot Smith – XO (1998)
Fiona Apple - extraordinary machine (2005)
Giant Drag - Hearts and Unicorns (2005)
Hole – Pretty on the inside (1991)
Interpol – Turn on the Bright Lights (2002)
Jeff Buckley - Grace ('Hallelujah' is a better version than Cohen's) -(1994)/John Frusciante - Shadows collide with people (2004) - (can’t decide between the 2)
K - Goldfish (2002)
Lemonheads - It's a shame about Ray (1992)
Mercury Rev - Yerself is steam (1991)
Nirvana - Bleach (1989)
Oberst, Conor (aka Bright Eyes) – I’m wide-awake, it’s morning (2005)
Pixies -Doolittle (1989)
Queens of the Stone Age – Rated R (2000)
Rufus Wainwright - Poses (2001)
Sonic Youth - Goo (1990)
The Breeders - Pod (1990)
Ultra Vivid Scene - Joy (1990)
Violent femmes - violent Femmes ('Why can't I get just one...') - (1982)
Whitestripes - Elephant (2003)
Yeah Yeah Yeahs - Fever to tell (2003)
Z – I have not ever been able to find an Indie band beginning with this letter!
