Only a marginal speed improvement (5-20%, compared to the respective given/when rewrite of your original version), but more of a memory usage optimization, i.e. not splitting the string into an extra array of letters, which consumes a lot more memory than the original string  (only relevant if the strings could be huge, though — in which case @A, @C etc. would be huge as well, of course...):

use 5.010;

for (my $i=0; $i<length($string); $i++) {
    my $letter = substr($string, $i, 1);
    given ($letter) {
        when ("A") { $A[$i]++; }
        when ("C") { $C[$i]++; }
        when ("G") { $G[$i]++; }
        when ("T") { $T[$i]++; }
        default    { $N[$i]++; }
    }
}
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P.S.: Perl 5.10's given/when is more than ten times as fast as the old (and generally frowned upon) switch/case.

Update:

#!/usr/local/bin/perl
use 5.010;
use Switch;
use Benchmark 'cmpthese';

$string = "AGCTAGCTAGAAGTCGGTGACTGfoobar";

sub orig_switchcase {
    my @seq = split(//,$string);
    my $i = 0;
    for my $letter (@seq) {
        switch ($letter) {
            case "A" { $A0[$i]++; }
            case "C" { $C0[$i]++; }
            case "G" { $G0[$i]++; }
            case "T" { $T0[$i]++; }
            else     { $N0[$i]++; }
        }
        $i++;
    }
}

sub orig_givenwhen {
    my @seq = split(//,$string);
    my $i = 0;
    for my $letter (@seq) {
        given ($letter) {
            when ("A") { $A1[$i]++; }
            when ("C") { $C1[$i]++; }
            when ("G") { $G1[$i]++; }
            when ("T") { $T1[$i]++; }
            default    { $N1[$i]++; }
        }
        $i++;
    }
}

sub substr_givenwhen {
    for (my $i=0; $i<length($string); $i++) {
        my $letter = substr($string, $i, 1);
        given ($letter) {
            when ("A") { $A2[$i]++; }
            when ("C") { $C2[$i]++; }
            when ("G") { $G2[$i]++; }
            when ("T") { $T2[$i]++; }
            default    { $N2[$i]++; }
        }
    }
}

sub BUK {
    my $string2 = $string;
    $string2 =~ tr[ACGT][N]c;
    $c{ substr $string2, $_, 1 }[ $_ ]++ for 0 .. length( $string2 )-1
+;
}

cmpthese(-1,
         {
             'orig_s/c'   => \&orig_switchcase,
             'orig_g/w'   => \&orig_givenwhen,
             'substr_g/w' => \&substr_givenwhen,
             BUK          => \&BUK,
         },
);

__END__
              Rate   orig_s/c   orig_g/w substr_g/w        BUK
orig_s/c    2112/s         --       -91%       -93%       -97%
orig_g/w   24660/s      1067%         --       -19%       -68%
substr_g/w 30632/s      1350%        24%         --       -60%
BUK        77422/s      3565%       214%       153%         --
[download]