use strict;
use warnings;

my @fileNames = ('file1.txt', 'foo.txt', 'wibble.wav');
my @fileHandles;

for my $filename (@fileNames) {
    open $fileHandles[@fileHandles], '<', $filename or die "Can't open $filename: $!";
}

while (@fileHandles) {
    for my $file (@fileHandles) {
        my $line = <$file>;
        
        if (! defined $line) {
            # Hit end of file
            close $file or die "File close failed: $!";
            $file = undef;
            next;
        }
        
        # do something with $line
    }
    
    @fileHandles = grep {defined} @fileHandles;
}