I found this list of the 50 Greatest American Independent Movies and have re-ordered it chronologically:
Shadows (1959) ⬇️
Night of the Living Dead (1968)
Easy Rider (1969)
Sweet Sweetback's Baadasssss Song (1971)
THX-1138 (1971) ⬆️
Two-Lane Blacktop (1971)
Mean Streets (1973)
Dark Star (1974)
The Texas Chain Saw Massacre (1974)
Eraserhead (1977)
Killer of Sheep (1977) ⬇️
The Evil Dead (1981)
Blood Simple (1984) ⬆️
Stranger Than Paradise (1984)
The Terminator (1984) ⬆️
Runaway Train (1985)
Blue Velvet (1986)
She's Gotta Have It (1986)
Evil Dead II (1987)
Matewan (1987)
Drugstore Cowboy (1989)
sex, lies, and videotape (1989)
Poison (1991)
Slacker (1991)
Bad Lieutenant (1992)
Reservoir Dogs (1992)
Dazed And Confused (1993)
Short Cuts (1993)
Clerks (1994)
The Usual Suspects (1995)
Lone Star (1996)
Swingers (1996)
Cube (1997)
Grosse Point Blank (1997)
In The Company Of Men (1997)
Happiness (1998)
Pi (1998)
Being John Malkovich (1999) ⬆️
Ghost Dog: The Way Of The Samurai (1999)
The Blair Witch Project (1999) ⬇️
Memento (2000)
Pitch Black (2000)
Donnie Darko (2001) ⬇️
Lost In Translation (2003)
Little Miss Sunshine (2006)
Juno (2007)
In Search Of A Midnight Kiss (2008)
The Wrestler (2009)
Winter's Bone (2010) ⬆️
Black Swan (2011)
Additional movies:
Nosferatu, A Symphony Of Terror (1922, Ger.)
Blood Feast (1963
Pink Flamingos (1972)
Mad Max (1979, Aus.)
Monty Python's Life Of Brian (1979, UK)
Bad Taste (1987, NZ)
Withnail And I (1987, UK)
Roger And Me (1989)
El Mariachi (1992)
Shallow Grave (1994, UK)
Buffalo '66 (1998)
Run Lola Run (1998, Ger.)
Amores Perros (2000, Mex.)
City of God (2002, Braz.)
Sideways (2004)
The Passion Of The Christ (2004, It./US)
The Descent (2005, UK)