One way would be to write a mod_perl auth handler...
Warning: Untestest code, but looks ok :)

package Apache::LogAuth;
use strict;
use Apache::Constants qw(:common);

sub handler {
  my $r = shift;
  my ($res, $sent_pw) = $r->get_basic_auth_pw;
  return $res if $res != OK;
  my $user = $r->connection->user;
  unless ($user && $sent_pw)
  { return AUTH_REQUIRED; }
  open(SOMELOG,">>somelogfile") || return DECLINED;
  print SOMELOG $user,"\n";
  close(SOMELOG);
  return OK;
}
1;
[download]

Ofcourse you can use $r->log->debug. The Apache config file should then contain something like

<LOCATION />
  AuthName Restricted
  AuthType Basic
  PerlAuthenHandler  Apache::LogAuth
  require valid-user
</LOCATION>
[download]

Another option is to just log $ENV{REMOTE_USER} with a script... but that doesn't specifically cover logins :)
Update: This is a mod_perl solution! If you don't have a clue about this, just forget it

Greetz
Beatnik
... Quidquid perl dictum sit, altum viditur.