A possibility is redrawing the whole screen at each frame. For instance (only tested on linux):

#!/usr/bin/perl -w

# Array containing all lines
my @screen = ( ' 'x70 . "\n" ) x 20;

# Array of possible (equiprobable) characters
my @char = split //, '                     *|';

while(1) {
    print join '', @screen;
    # Drop last line
    pop @screen;
    # Put a new line on top
    unshift @screen, join ( '', map { $char[ rand(@char) ] } (1..70) )
+ . "\n";
    # Sleep for 0.1 seconds
    select(undef, undef, undef, 0.1);
}
[download]

Update: The value 20 in the @screen initialization should be at least the terminal height minus 1 (due to the last line being empty). If it's less, then the upper portion of each frame is filled by the last lines of the previous one.

So, incorporating abell and cfreak's suggestions, you get:

#!/usr/bin/perl -w

@screen = ( ' 'x70 . "\n" ) x 20;
$gen_line = sub {
    my $qw;
    for(1..70){
        if( !$q[$_] && rand > .993 ){
            $q[$_] = q$.$ x 5 . q$ $ x 1 
                . ${ [ qw$tsuJ rehtona lreP rekcaH$ ] }[$qq++]
                . q$ $ x 1 . q$.$ x 5;
            $qq = $qq > 3 ? 0: $qq;
        }
        if( $q[$_] ){
            ( $qx, $q[$_] ) = split//, $q[$_],2;
            $qw .= $qx;
        }else{
            $qw .= q$ $;
        }
    }
    "\33[0;32m$qw\33[0m";
};

while(1) {
    print join '', @screen;
    # Drop last line
    pop @screen;
    # Put a new line on top
    unshift @screen, $gen_line->() . "\n";
    # Sleep for 0.1 seconds
    select(undef, undef, undef, 0.1);
}
[download]

Cool, monks! =]


cp
----
"Never be afraid to try something new. Remember, amateurs built the ark. Professionals built the Titanic."

Seems to work nicely under ActiveState Perl 5.8.0 on Windows 2000.

---

"Ex libris un peut de tout"