With all due respect, I think you should avoid ysth's guess about the matter -- his advice would obliterate the input file, and you don't want that (unless you have a backup copy somewhere).

The problem is that you need to do binmode on STDOUT, as well as on FILE (the input file handle):

#!/usr/local/bin/perl

chdir ("d:\\www\\mypage.net\\www\\test\\");
$zipfile = "zipfile.zip";

print "Content-type:application/x-zip-compressed\n\n";

open FILE, "< $zipfile";
binmode FILE;

binmode STDOUT;  ## add this
$/ = undef;  ## use slurp mode for input, too

print <FILE>;

# closing both FILE and STDOUT is automatic at end-of-script
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update: If you're going to be dealing with really big zip files (I'm guessing 2 MB might be a practical limit), you might opt for fixed-length read/write instead of slurp-mode (taking the whole file into memory at once and printing it all at once). In any case, don't rely on the "default" value of $/ (input record separator), since there's no telling what sort of read/write sizes you'll get that way. Set $/ to a reference to a sensible integer value to control the number of bytes read from FILE:

$/ = \16386 # (d'oh!)

$/ = \16384;  # 16 KB/read 

while (<FILE>) {
    print;
}

# It's not a problem if the last "record" read from FILE is <16 KB.
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(another update: I agree with Jaap about the chdir thing.)