Where can I find up-to-date statistics on the number of web sites on a
year to year basis from 1990 to 2003?

Hello.

Mosaic, the revolutionary browser for viewing web sites, was actually
launched in 1993.

As a result, the data about the number of "web sites" actually began
to be compiled in June 1993. Thus, I'll give you the year-to-year data
for June '93 - June '02, plus January '03.

WWW Growth (Number of web sites):
06/93         130
06/94       2,738
06/95      23,500
06/96     252,000
06/97   1,117,259
06/98   2,410,067
06/99   6,177,453
06/00  17,119,262
06/01  29,302,656
06/02  38,807,788
01/03  35,424,956

Sources: Hobbes Internet Timeline: WWW Growth
http://www.zakon.org/robert/internet/timeline/

Netcraft.com: June 2002 data
http://www.netcraft.com/Survey/index-200206.html

Netcraft.com: January 2003 data
http://www.netcraft.com/Survey/index-200301.html

If you're interested in the number of "internet hosts" rather than
"web sites," Hobbes Internet Timeline has data beginning in December
1969 when there 4 internet hosts:
http://www.zakon.org/robert/internet/timeline/#Growth

search strategy: "number of web sites", 1993, 1994, 1995, 1996, 1997,
etc

I hope this helps.