Speaking as a trained archivist who works in this field, the answer is yes, classified materials are destroyed regularly. All records created by the Government are described by a records schedule which indicates how long the records need to be retained, and also the classification level of the records. Just because a record is classified, doesn't mean that it needs to be retained forever. Permanent retention is reserved for records of enduring legal, historical, or other value.

There are regularly scheduled shredding and burn runs for records being destroyed, and meticulous records are kept along the way. Records in electronic form, CDs, tapes, etc. are destroyed appropriately as well.

It's not my department, but I believe the records schedules are all publicly available (at least to FOIA) and all records scheduled for non-permanent retention are first published in the Federal Register.

So before a record is destroyed, it is first examined by an archivist, it's potential historical value assessed and a retention schedule created which indicates for how long the agency needs to retain the information. Generally there are legal reasons which dictate how long records are retained (for example, tax returns are kept for a certain period of time and then destroyed.)

Once the retention period is over, agencies are free to destroy the records. Occasionally the agency will turn over long-term temporary records to the National Archives, who will retain the records for a period of time, and then destroy the records. Temporary records are usually destroyed by the agency (for example, routine office correspondence, internal memos, etc.)

Classified records are handled in the same manner as non-classified records, but with higher security precautions. For example, to properly destroy compact discs with classified material on them, the CDs are face grinded by a specific machine, and this is witnessed and attested to by two employees with security clearances, the CDs are then burned.

Of course mistakes might be made in destroying material that should have been considered valuable, it's hard to know exactly what will be valuable in the future, but archives tend to err on the side of retaining too much information. The vast majority (ca. 95%) of records retained by the U. S. National Archives is never viewed by anyone, despite being freely available.