Anti-Climacus

A Guide for the Lost Indie Culture, in 25 Albums:

Kids, you may not believe this, but we had indie music back in my day, too. And it was better, if only because it was part of a decades-long historical narrative that culminated in actual commercial success for some of the bands we liked. It has occurred to me that this narrative has been lost, and you mostly listen to things we would have derisively snickered at had you attempted it back in the day (we listen to that same music, but we're old, so it's different. do you really want to be like old people?). I assume a knowledge of oldies and classic rock radio, so I don't have to spend time explaining who, say, The Beatles or Led Zeppelin were (though I might have to spend some time explaining why they're terrible). So herewith, a guide to what's good for you:

The forefathers:
Rolling Stones, Exile on Main St.
Velvet Underground, The Velvet Underground & Nico
Iggy and the Stooges, Raw Power

Punk and the acceptable mainstream alternatives to punk of the late 70s, by which I mean David Bowie who, yes, was mainstream, even when he was making weird coked-out ambient albums in Berlin
Patti Smith, Horses
David Bowie, Low
Television, Marquee Moon
Wire, Pink Flag
Gang of Four, Entertainment! 

'Murrica/our band could be your life
R.E.M., Murmur
The Replacements, Let It Be
Hüsker Dü, Flip Your Wig
Minutemen, Double Nickels on the Dime 

British before britpop
Joy Division, Unknown Pleasures
The Smiths, Hatful of Hollow
Stone Roses, The Stone Roses

The rise of alternative:
Jane's Addiction, Ritual De Lo Habitual
Sonic Youth, Dirty
Liz Phair, Exile in Guyville
PJ Harvey, Rid of Me
Pavement, Crooked Rain, Crooked Rain
Guided By Voices, Bee Thousand

Radiohead used to play actual pop songs. they were pretty good, too. and the answer to 'blur or oasis?' is 'pulp.'
Radiohead, The Bends
Pulp, Different Class

Odds and ends:
Yo La Tengo, I Can Hear the Heart Beating as One
Neutral Milk Hotel, In the Aeroplane Over the Sea
Sleater-Kinney, Dig Me Out
Belle and Sebastian, The Boy With the Arab Strap