Let's say that through community development on a repository, some files are accidentally deleted. How would we get the old files back?

The correct collection of files is as follows:

lab46:~/src/backgammon/queue$ ls
Makefile   create.cc   destroy.cc   queueops.cc
lab46:~/src/backgammon/queue$ 

First, we should try and narrow down the range of revisions where the problem was introduced:

lab46:~/src/backgammon$ svn log
------------------------------------------------------------------------
r353 | jbrant | 2010-11-12 11:19:40 -0500 (Fri, 12 Nov 2010) | 1 line

clean up of /queue
------------------------------------------------------------------------
r352 | jbrant | 2010-11-12 11:18:25 -0500 (Fri, 12 Nov 2010) | 1 line

clean up of /queue
------------------------------------------------------------------------
r351 | jbrant | 2010-11-12 11:16:54 -0500 (Fri, 12 Nov 2010) | 1 line

clean up of /queue
------------------------------------------------------------------------
...

Through an analysis of the log, and having an understanding of the time range at stake (it was there yesterday), it would seem we have a range of revisions where this problem was introduced.