Non recursive implementation, strict safe, but not warning free. 252 chars.

use strict;

sub spiral {
my$S=pop;my($z,$s,$t,$d,$x,$y,@b)=($S**2,1);@_=([1,
0],[0,1],[-1,0],[0,-1]);$b[$S][$_]=$b[$_][$S]=$/for
0..$S;map{$b[$y][$x]=sprintf"%0*d",length$z,$_;($s,
$t)=@{$_[++$d%4]}if$s&&$b[$y][$x+$s]||$t&&$b[$y+$t]
[$x];$x+=$s;$y+=$t}1..$z;pop@b;print"@$_"for@b;
}    
     
for (1..10) {
    spiral($_);
    print "\n---\n";
}
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It could go smaller fairly easily by using globals, but then couldnt be run more than once per process.

Update: And here is the annotated version. Funny, while annotating it I noticed a couple of things I could have done to make it smaller :-)

use strict;

sub spiral {
    my $size = pop;          # get the size from the arguments
    my $elements = $size**2; # how many numbers in the square
    my $dir=0;               # we will go right at start 
    my ($dx,$dy)=(1,0);      # starting deltas (must match $dir)
    my ($x,$y)=(0,0);        # start top left
    my @board;               # the board we will use
    my @delta=([1,0],        # deltas for going right 
               [0,1],        # ... down
               [-1,0],       # ... left 
               [0,-1]);      # ... up
               
    # Set up sentinal values in (x,$size) and ($size,y)
    # ie, a column on the right and a row at the bottom
    $board[$size][$_]=$board[$_][$size]="\n"
        for 0..$size;
    
    # The strategy is to treat $x,$y as a cursor on the grid.
    # each square we move in the direction specified by $dir
    # via the @delta table, assuming that is that the new
    # cell has not been filled already. if it has we turn to
    # the right by incrementing $dir and finding new deltas.
    for (1..$elements) {
        # neatly set up the value in the grid, we use the length of 
        # the center element to determine how many digits to use per "
+cell"
        $board[$y][$x] = sprintf"%0*d",length $elements, $_;
        
        # if we bump into something we need to turn to the right
        # the sentinals mean we dont have to check for anything other
        # than the cell being nonempty in the direction we are travell
+ing
        ($dx,$dy)=@{$delta[++$dir%4]} 
            if $dx && $board[$y][$x+$dx] 
            || $dy && $board[$y+$dy][$x];
        # and adjust our position according to the deltas
        $x+=$dx;
        $y+=$dy
    };
    
    # we need to remove the bottom row as it is just a list of newline
+s
    pop @board;  
    # and now we print it out, we dont need to remove the right hand 
    # sentinals as they conveniently end the line for us.
    print"@$_" for @board;
}    
     
for (1..10) {
    spiral($_);
    print "\n---\n";
}
[download]