##
$textfield =~ s/\015\012|\015|\012//g;
If you prefer hex to octal :-)
$textfield =~ s/\xD\xA|\xD|\xA//g;
####
In expanded commented /x form:
$textfield =~ s/ # substitute
\015\012 # a CRLF sequence (DOS, MIME...)
| # or
\015 # a lone LF (mac)
| # or
\012 # a lone LF (unix)
/ # with literal ''
/xg; # /x allow comments, /g do globally