In order to efficiently troubleshoot problems involving failed setup, we need to use the setup logs. Once you know where the log files are located, you can start troubleshooting. What to look for in the log files is a separate topic in itself, but at least if you know where the log files are, then you can attempt to look for logical clues in the files. So, where are these log files located? Here's a summary, listed by product and version. I took some efforts to compile the list of available rollup hotfixes and their relevant KB articles, hopefully that in itself is a very useful thing.
So, I hope the list and the notes below are very useful for you; please feel free to rate the article and provide comments as well!
Product Major Version 1
Product Level 2
Version post setup 3
Bulletins / KB Articles
Location of setup logs 4
SQL Server 2000 (8.0)
Post-SP4 GDR security rollup 7
[Recommended] Post-SP4 QFE security rollup 8.a
%WINDIR%\SQL2000-KB948111-v8.00.2273-x86-ENU.log; SQLServerClient_Hotfix_KB948111_*.log 11
IA64 versions of the security rollups 13
Per respective packages mentioned above
Clustered instance 14
%WINDIR%\sqlstpN.log from both nodes
Service Pack only:
%WINDIR%\sqlspN.log from both nodes;
%WINDIR%\remsetup.log from active node
Relevant hotfix files as described above from both nodes
SQL Server 2005 (9.0)
%ProgramFiles%\Microsoft SQL Server\90\Setup\Bootstrap\LOG\Files
%ProgramFiles%\Microsoft SQL Server\90\Setup Bootstrap\LOG\Hotfix; files will have KB921896 as part of their name.
Post-SP2 GDR security rollup (engine only)
Same as above; files will have KB948109 as part of their name.
Post-SP2 GDR security rollup (engine + Reporting Services)
Same as above; files will have KB954606 as part of their name.
Post-SP2 QFE security rollup (engine only)
Same as above; files will have KB948108 as part of their name.
Post-SP2 QFE security rollup (engine + Reporting Services)
Same as above; files will have KB954607 as part of their name.
CU #11 for SP2 8
Same as above; files will have KB958735 as part of their name.
Same as above; files will have KB955706 as part of their name.
CU #1 for SP3 8
Same as above; files will have KB959195 as part of their name.
%WINDIR%\tasks\SchedLgU.Txt 6; Setup bootstrap will copy all the files from remote node to active node.
SQL Server 2008
%ProgramFiles%\Microsoft SQL Server\100\Setup Bootstrap\Log 9
At the time of writing no special considerations are known.