Another (and less efficient) way, using Tie::File:

use strict;
use warnings;
use Tie::File;

my @fnames = @ARGV;
my @fhandlers;

for my $fname (@fnames) {
  tie my @farr, 'Tie::File', $fname or die $!;
  push @fhandlers, \@farr;
}

# Traverse the files:
for my $i (0..$#{$fhandlers[0]}){ 
  my @nextvals = map {$_->[$i]} @fhandlers[0..$#fhandlers];
  # @nextvals has the next line of each file
}

untie $_ for (@fhandlers);
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Beware of possible overheads if the files are very big. (0..$#{$fhandlers[0]}) traverses the whole first file just for know how many lines it has.

Update: Added note about efficiency