Yes, for a while anyway. In Minnesota, a corporation (associations are non-profit corporations) must keep complete copies of its governing documents, accounting records, voting records and all minutes of meetings of the members, of the board and of any committee that has the authority of the board for six years. Anything older than that can be discarded from a legal standpoint.
However, although you can discard information older than six years, many associations find that it is inexpensive and easy to maintain records for longer. Your binders full of paper can be reduced to electronic format and stored on a flash drive, DVD or even your association website (but please password protect your financials!). By utilizing electronic storage of documents, you will be able to retain documents well past the six-year minimum. This may be useful in the future to see how an issue was addressed previously.