If you really want to get the long answer on 2000 vs 2001 being the start of the milleninum, check out:
http://www.countdown2000.com/body_a_moment_in_time.html
The short answer is: It depends on who you ask. I stick with conventional wisdom and believe it starts in 2001. 2001: A Space Odyssey is my favorite movie so I'm biased <g>
Some answers I saw listed on a linked page:
When does the millenium arrive?
1. The year 2000 only (and especially: Midnight, January 1, 2000)
2. The year 2001 only (and especially: Midnight, January 1, 2001)
3. The years 2000 and 2001 (or as much as the entire two years)
4. As long and as much and as soon as possibly justifiable
5. Beginning approximately or precisely March 13, 1997
6. Beginning approximately or precisely December 25, 1996
7. All the years 1996 to 2003 (or as much as eight full years)
8. The years 1996-1997 most especially (palindromic corroboration)
9. The years 1996-1997 most especially (traditional corroboration)
10. The third, seventh and first sabbatical Millennium all together
11. Proposed calendrical reform to acknowledge all three new Millenniums
12. The years 1990-3004 (or as much as 1015 years of continuous Christmas)
[This message has been edited by dg1 (edited 12-11-1999).]