The Minotaur Series of rockets developed by Orbital Sciences corporation probably incorporate some of the oldest bits of hardware currently launching things into space. The Minotaur 1 is based on old Minuteman II boosters, while the Minotaur IV uses old Peacekeeper boosters.
These use missiles which were decommissioned and placed in storage decades ago, but with some quality checks they're cleared to fly again and carry government payloads into space.