Use this with caution. rename will destroy any file that gets in its way. Also, you don't need that =~ in front of the s///:

for ( glob "*.abc" ) 
{
   my $old = $_;
   s/\.abc$/.edf/; 
   rename $old, $_ or warn "can't rename '$old' to '$_'";
}
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Update:
Ok, I looked again at stefp's code and I see why that =~ was there. If you use that method, don't forget to declare $new somewhere... (you are using strict, aren't you?) and of course, you might want to add some code to make sure rename isn't going to delete anything. maybe:

for( glob "*.abc" )
{
    my $new = $_;
    my $ok = 1;
    substr $new, 0, -3, "edf";
    if( -e $new )
    {
        warn "file '$new' already exists. Do you want to replace?\n";
        while(<STDIN>)
        {
            last if /[yY][eEsS]{0,1}/;
            $ok = 0, last if /[nN][oO]{0,1}/;
            warn "Yes or No?\r";
        }
    }
    
    rename $_, $new or warn "can't rename '$_' to '$new'\n " if $ok;
}
[download]

That is untested...