all a matter of taste...
With out a doubt, "Jules and Jim" is one of the finest films I have ever seen...heck it ranks as one of the best films of all time. Its older (62) but is a film worth seeing.
Honestly the best list to date is from imdb...
http://indie.imdb.com/chart/independent
Now many of those are older but take a look and you can see some of the great indies.
If you want to really see the "deep" and "meaningful" films look into some foreign films....french, Spanish, and Italian more specifically. They have brought some of the huge indie bombshells (in a good way) to be.