Everything by John Hughes and Spielberg from that time frame.
Pretty much what everyone else has mentioned.
Singles - This Cameron Crowe movie really captures the whole Seattle scene of the 90's. Great soundtrack. Sort of a John Hughes movie with more adult characters.
Grifters - a very dark movie with some wonderful acting in it by John Cuzak and Annette Benning.
The Crow - The death of Brandon Lee during the making of this film made the story all the more powerful and tragic. You'll tear up from realizing what might have been.
Tombstone - Best western movie of the 90's.
Dances with Wolves - most over hyped western of the 90's, but still a very good movie.