Championship Results on the Web

Olympic Games

Complete results of all Games are available here:
Olympedia.org - IOC-approved site run by the Olympic MADmen, mostly members of the International Society of Olympic Historians (ISOH), including Bill Mallon

Official Reports, containing results to various degrees of completeness are available from the LA84 Foundation.
PDF documents here are large and quite slow to download.
Photo-finish times are only included from 1972 onwards.

World Athletics (formerly the IAAF) still maintains the results for the most recent Olympic Games:
2000 Sydney
2004 Athens
2008 Beijing
2012 London
2016 Rio de Janeiro

Commonwealth Games

Up to 1998, basic results are available on the Commonwealth Games Federation web-site. Search results by: Sport, choose Athletics and an Event and you can then select a year to see the results in the final round contested by each participant.
From 2002 complete results are still online if you can find them:
2002 Manchester
2006 Melbourne
2010 Delhi (slow site)
2014 Glasgow
2018 Gold Coast results book

IAAF Competitions

All IAAF Meetings - this includes Grand Prix meetings, Combined Events Challenge meetings, etc

Some links there are broken, so corrected links include:
1983 Helsinki (no field event series, no combined events details)
1987 Rome (no field event series, no combined events details)
1991 Tokyo (no field event series)
1993 Stuttgart (no field event series)
1995 Gothenburg (no field event series)
1997 Athens
1999 Seville
2001 Edmonton

For meetings 1988-1992 the IAAF published 4 booklets with basic results (no field event series)
For meetings 1992-2007 the IAAF has published 4 books with comprehensive results and these are still available:
IAAF Publications

Junior Championships

World Junior Athletics History by Lionel Peters & Tomas Magnusson

European Competitions

Results back to 2005, to various degrees of completeness, are in the EAA's Results Archive

Results by year can be found on the Internet Archive:
2002
2003
2004

European Championships

For better results of European Championships, use the following links:
2002 Munich
2006 Gothenburg
2010 Barcelona (also PDF files by date)

Some earlier auto-times can be found here on the NUTS web site

French Results

FFA Archives going back to 1999
Archive of international matches back to 1999
Search their archives back to 2004
Search their archives 1997-2003

Spanish Results

Atletismo en Espana archived bulletins 1992 to 2000 and 2005 onwards