The lack of any way to preserve file timestamps has made git a total non-starter for me. Mercurial has the TimestampMod extension (http://mercurial.selenic.com/wiki/TimestampModExtension).
Like others have said though, I don't understand what a use case for this would be. The page for that Hg plugin seems to indicate that it is just meant to ease the transition to version control, for users who don't yet 'get it'.
I will say that file timestamps invoke horrible, horrible memories of an employer that used Visual Source[un-]Safe -- a VCS that relied on accurate client system time for history integrity. I.e. the repo was easily corrupted if a client wasn't on synchronized time. Also, race conditions. AFAICT, it met none of the conditions casually denoted by the words "Version Control System".