Hi all again,
Thanks for the great input. Based on your comments, I've given the code another go. This time I've "compiled" the code into the form (op_name, arglist...), which is then run using an "eval". I've also establised a symbol table hash (which currently holds the lvalue type and value). I'd like to have your opinion on this design. (Oh yeah, the grammar syntax is still very ugly and basic. Needs to be redone.)
Thanks for your time.

use Parse::RecDescent;
use vars qw(@lines $curline %stash);
use strict;

$RD_HINT++;
$RD_WARN++;
#$RD_TRACE++;


sub do_print
{
    my $a=shift;
    print "$a\n";
}

sub do_goto
{
    $curline = int(shift)-1;
}

my $grammar = q{
  Start: Expression(s) /\Z/
  Expression: LineNum Print
  { 
      $::lines[int($item{LineNum})]= ["print", [$item{Print}]];
  }
  | LineNum Goto
  {
     $::lines[int($item{LineNum})]= ["goto", [$item[2]]];
  }
  | LineNum Ass
  | <error>
  Ass: StringAss
  | NumAss
  StringAss: Identifier /\$/ /=/ /\"/ String /\"/
  {
      $::stash{$item{Identifier}}{type}="String";
      $::stash{$item{Identifier}}{value}=$item{String};
  }
  NumAss: Identifier /=/ Number
  {
      $::stash{$item{Identifier}}{type}="Number";
      $::stash{$item{Identifier}}{value}=$item{Number};
  }
  Goto: /goto/i LineNum
  Print: /print/i /\"/ String /\"/
  { 
      $item{String};
  }
    | /print/i Identifier /\$/
    {
    if(defined($::stash{$item{Identifier}}{value}))
    {
        $::stash{$item{Identifier}}{value};
    }
    else {die "A nasty and horrible death... Bad string identifier.\n"
+;}
    }
    | /print/i Identifier
    {
    if(defined($::stash{$item{Identifier}}{value}))
    {
        $::stash{$item{Identifier}}{value};
    }
    else {die "A nasty and horrible death... Bad number identifier.\n"
+;}
    }
  String: /[\w\s]+/
  LineNum: /\d+/
  Identifier: /[a-zA-Z][a-zA-Z0-9]*/
  Number: /[+-]?\d+(\.\d+)?/
  };

my $parser = new Parse::RecDescent($grammar);
undef $/;
my $text = <>;
$parser->Start($text);
$curline=0;

while(1)
{
    if($lines[$curline])
    {
    my $todo = "do_".${$lines[$curline]}[0]."(\"";
        my $args = join(', ', @{${$lines[$curline]}[1]});
        $todo = $todo.$args."\")";
        eval $todo;
    }
  last if $curline>$#lines;
  $curline++;
}
[download]

Here are some test files:
test1.bas

5 print "This "
10 print "is "
15 print "a "
20 print "test"
25 goto 5
[download]

test2.bas

5 a$ = "This is a string"
10 print a$
15 b = 35
20 print b
[download]