For one thing, your code doesn't run:

Can't use global $_ in "my" at /tmp/tst line 4, near "my $_ "
Execution of /tmp/tst aborted due to compilation errors.
[download]

For another, all you're doing with that "map" statement is returning (via $_) the return of the substitution statement ('1') rather than the modified value of $_ - printing "@fields" would be instructive here.

Lastly, you're explicitly splitting $_ inside your loop; changing the iterator variable is thus going to leave $_ empty, which means that your code isn't going to work. Here's a slightly simpler version of your code, both with an explicit iterator and without:

#!/usr/bin/perl -w
use strict;

for my $foo (<DATA>) {
    my @fields = grep { s/^\s+|\s+$//g; 1; } split /\|/, $foo;
    print "$fields[1]\n";
}

__END__
Baw|Vao|111 Noa St||NewYork|NY|10012|2123456789|123456789
Vca|Wxr|384 Mkl Ln|Xillo|Crrnt Stt|CT|05506|1015567781|1015567782
Uaa|Kvbr|805 Test Rd|Zero|This St|MN|17205|3018757203|3012986736
Caa|Lvbr|905 Test Rd|Bero|That St|MD|12705|3028887203|3028886736
Eaa|Pvbr|311 Zest Rd|Tero|My St|MI|12505|3018757203|3012986736
[download]

#!/usr/bin/perl -w
use strict;

for (<DATA>) {
    my @fields = grep { s/^\s+|\s+$//g; 1; } split /\|/;
    print "$fields[1]\n";
}

__END__
Baw|Vao|111 Noa St||NewYork|NY|10012|2123456789|123456789
Vca|Wxr|384 Mkl Ln|Xillo|Crrnt Stt|CT|05506|1015567781|1015567782
Uaa|Kvbr|805 Test Rd|Zero|This St|MN|17205|3018757203|3012986736
Caa|Lvbr|905 Test Rd|Bero|That St|MD|12705|3028887203|3028886736
Eaa|Pvbr|311 Zest Rd|Tero|My St|MI|12505|3018757203|3012986736
[download]

The output in both cases is:

Vao
Wxr
Kvbr
Lvbr
Pvbr
[download]

Update: I just noticed one more thing: you're using "\r" when you're printing - which means that you're going to overwrite every line that you print. This means that you'll only see the last line, plus anything left over (i.e., anything that was past the current last character) from the previous lines. The correct character to use, at leat in the Unix world, is "\n"; for DOS-based systems, "\n\r" is appropriate.