<p>Are SQL Server timeouts (SELECT queries, in particular) logged in the ERRORLOG file?</p>

<p>Background is a customer with a web site having occasional "Request timeout" messages, looking to me assuming that the timeout is caused by a database timeout.  There are no timeout errors in the ERRORLOG in question.</p>

No. You will need to use SQL Profiler. A standard trace with the
Lock Timeout
event and
Deadlock Graph
events should do it.
Lock:Timeout Event Class
Deadlock Graph Event Class
Hardware aside (such as enough RAM and fast drives, and appropriate placement of Data and Log files on the appropriate RAID configurations) most timeouts are caused by not having a sufficently 'good' set of indexes for your workload.
Do you have index maintenance plans scheduled regularly?