my @files= qw| /path/to/file1 /path/to/file2 /path/to/file3 |;
my @allfiles;
for my $filename(@files){
    open FILE, $filename ||
        die "Cannot open $filename for reading: $!\n";
    push @allfiles, $_ while (<FILE>);
    close FILE;
}

# Or (and even more Perlish) ...

my @files= qw| /path/to/file1 /path/to/file2 /path/to/file3 |;
my @allfiles;
for my $filename(@files){
    open FILE, $filename ||
        die "Cannot open $filename for reading: $!\n";
    push @allfiles, <FILE>;
    close FILE;
}