1984-1990:
The numbers between 1984 and 1989 are largely based on estimates mentioned in articles and also in reports. These estimates range roughly from 30 to 55 attacks each year.
The Federation of American Scientists (FAS) has published annual reports of piracy incidents from 1985 to 1999. These Anti-Shipping Activity Messages are collected and available at the website of the FAS. The pages on the FAS website have been created by using the Anti-Shipping Activity Messages Database which is created and maintained by the National Imagery and Mapping Agency (NIMA) and the Maritime Safety Information Centre (MISC) for the US Maritime Administration (MARAD) government agency. Not included in my statistics are warnings that have also been included as ASAM-records in the database.

1991-1999:
IMO provides information on the total number of incidents of piracy and armed robbery reported to the organization since it began compiling statistics on these unlawful acts in 1984. The Piracy Reporting Centre was established in 1992 and has since then also been compiling and distributing information on piracy incidents ; they had amounted to 1,543 by the end of September 1999. In the 1998 annual report of the IMB an overview is presented of 1991 - 1998. The total number of attacks for these years is 1261. In the quarterly and monthly reports of the IMB in 1999 (up to November) 217 incidents are reported. Deduct this total from 1587 and the number of incidents that remains is 109.
In the reports by the UN Secretary General over 1993-1999 a seperate section is devoted to Piracy and armed robbery. The numbers in these reports are also included in the overview. From the end of November to the end of December the International Maritime Bureau has published Weekly piracy reports. The total number of attacks reported in these reports are 27. The total number of reported incidents from the monthly and weekly reports is 244. After publication in January 2000 the total number of incidents is reported in the annual report by the International Maritime Bureau is 285.
The annual piracy report of 2000 also contains an updated total of piracy incidents for 1998: 202. At the beginning of each year an annual report is published by the International Maritime Bureau. The total number of incidents for this year is published but usually this total number needs to be corrected after several months when new piracy incidents for the previous year are (belatedly) reported. Example: this means, for instance, that the total number for 1999 will need to be corrected during the first few months of 2000. This is the case each year. 315 incidents and 20 warnings have been reported for 2000 in the IMB Weekly Reports. Right now the last known number for 2000 can be found in the annual piracy report of the IMB, published in January 2001: 469. This is an alltime record number of reported incidents. The International Maritime Organization has published 12 Monthly reports in 2000 and the total from this organization is: 427. In the 2001 Annual Report of the IMO, published in March, the total number is: 471.

Sources:

1. The growing threat of piracy / Thomas B. Hunter
   In: Proceedings - Unites States Naval Institute, ISSN 0041-798X, vol.125 (1999 July 1) nr.7, P.: 72
2. Das piratenunwesen nimmt weltweit dramatisch zu
   In: Schiff & Hafen, vol.51 (1999) nr.2, P.: 9-13
3. Piracy and armed robbery against ships - annual report: 1st January-31st December 1998. - Barking, United Kingdom : ICC International Maritime Bureau, Piracy Reporting Cenre, 1999 January
4. Piracy and armed robbery against ships - annual report: 1 January-31 December 1999. - Barking, United Kingdom : ICC International Maritime Bureau, Piracy Reporting Cenre, 2000 January
5. Shippers pay for piracy protection: Brazil, Thailand and India introduce programs to stop pirate attacks in ports
   In: American Shipper, vol.40 (1998 May) nr.5, P.: 80
6. Maritime piracy Reaches record
   In: Reuters News Service (1997 Feb 3)
7. Yohoho en een fles mer rum: moderne piraten / Jippes Hieke
   In: NRC Handelsblad (1997-11-25) Saturday Suppl.
8. Piracy today: robbery and violence at sea since 1980 / Roger Villar. - London : Conway Maritime Press, 1985
9. Scourge of piracy returns to Southeast Asia / Tammy Arbuckle
   In: International Defense Review, vol.29 (1996) nr.8, P.: 26-29
10. Violent attacks increase : report reveals worrying trend
    In: Fairplay International (1996-02-22), P.: 27/28
11. Piraterij op zee neemt toe
    In: Brabants Dagblad (1995)
12. General Assembly, Fourty-ninth - Fifty-fourth session, 1994-1999 - Reports of the Secretary-General. - section: Piracy and armed robbery (1994-1999). - Division for Ocean Affairs and the Law of the Sea, Office of Legal Affairs, United Nations, 1994-1999
13. 1985 - 1999 Anti-Shipping Activity Messages (ASAM) / John Pike. - Federation of American Scientists. - (Anti-Shipping Activity Messages). - Downloaded on: 2000 Aug 4
14. Anti-Shipping Activity Messages (ASAM). - National Imagery and Mapping Agency, 2001 Sept 14
    Source: http://164.214.12.145/asam/asam_i_query.html
15. Piratical attacks including the seizure of vessels for ransom - seafarers view / Noor Apandi Osnin, Choy Ngee Sheng. - Kuala Lumpur : Maritime Institute of Malaysia, 1998 June [?]
    Source: http://www.mima.gov.my/htmls/depts/pdf/pirate.pdf
16. Piracy and armed robbery against ships - annual report: 1 January-31 December 2000. - Barking, United Kingdom : ICC International Maritime Bureau, Piracy Reporting Cenre, 2001 January
17. Annual report on acts of piracy and armed robbery against ships 2000. - London : International Maritime Organization. Maritime Safety Committee, 2001 March 31. - (Piracy and armed robbery against ships - annual report ; MSC/Circ.991)