The oldest satellite still orbiting in April 2000 was the tiny – 1.4 kg 3 lb 1 oz – Vanguard 1 (USA), which was launched on 17 Mar 1958. Although no longer operating, it continues to orbit.
Vanguard I is also the oldest piece of orbital space debris. [Source: National Geographic, “Clearing Space”, Michael D. Lemonick, pp.30-33, July 2010]
Note by consultant Mark Aston (October 2011): This is still valid. 17th March 2008 was Vanguard One’s 50th anniversary in orbit.