'Indie' is such a broad definition incorporating many offshoots of the post-punk era (Britpop, shoegaze, indie rock, lo-fi, etc) and nowadays seems to be some kind of umbrella term for anything with guitars in it that isn't metal...?
But I guess if I was forced at gunpoint to choose a few 'proper' indie groups off the top of my head:
There are so many denominations of 'indie' (lo-fi, shoegaze, indiepop/C86, indierock etc) that it's a bit difficult to pin down your faves without omitting plenty. That, and the fact that 'indie' these days seems to be an umbrella term encompassing any old **** with electric guitars that isn't metal...?
However if you held me at gunpoint I suppose I'd blurt out these youtube links:
1. My Bloody Valentine
2. Pixies
3. Silversun Pickups
4. Dinosaur Jr
5. The Smiths
6. Echo and the Bunnymen
7. Radiohead
8. The Jesus and Mary Chain
9. The Stone Roses
10. Slowdive