Description:
Under unix doing the passwords like the below appears to be a standard approach.
Does having /usr/lib/libcrypt.a by cygwin help? If so, pls enhance the documentation accordingly!

Thx Ralf
====================================================
mysql> update TBL_USER set password= encrypt('holderio', '$1$saltsalt$') where login= 'ameyer';
Query OK, 1 row affected (0.00 sec)
Rows matched: 1  Changed: 1  Warnings: 0

mysql> select encrypt( 'testpassword', password) = password from TBL_USER where login='ameyer';
+-----------------------------------------------+
| encrypt( 'testpassword', password) = password |
+-----------------------------------------------+
|                                             0 |
+-----------------------------------------------+
1 row in set (0.00 sec)

mysql> select encrypt( 'holderio', password) = password from TBL_USER where login='ameyer';
+-------------------------------------------+
| encrypt( 'holderio', password) = password |
+-------------------------------------------+
|                                         1 |
+-------------------------------------------+
1 row in set (0.00 sec)

How to repeat:
under windows, it fails.

Suggested fix:
enhance the documentation how to configure mysqld to benefit from libcrypt.a or /usr/bin/crypt.exe accordingly

I extended the manual documentation a bit:

If crypt() is not available on your system, ENCRYPT() always
returns NULL.  Becasue of this we recommend you to use MD5()
or SHA1() instead as these exists in all platforms.

The above is a much better solution than try to get crypt() from cygwin to work with MySQL.

1) I do have crypt!
Microsoft Windows 2000 [Version 5.00.2195]
(C) Copyright 1985-2000 Microsoft Corp.

C:\>crypt
usage: crypt passwd
       crypt salt passwd

C:\>crypt saltsalt holderio
samNJTG7AOcqs

C:\>

2) If I use MD5, does this also have the nice feature that both salt and digest get stored in the standard way in the database?

$1$saltsalt$i9cJkDelJCZ5584r0rxAQ/

or would I rather have to look for cygcrypto.dll as per http://www.cygwin.com/ml/cygwin/2003-07/msg00252.html

-rwxr-xr-x    1 rhauser  mkgroup    868352 Apr 11 12:34 /usr/bin/cygcrypto-0.9.7.dll
-rwxr-xr-x    1 rhauser  mkgroup    660480 Apr 11 12:37 /usr/bin/cygcrypto.dll

Sorry, but the bug system is not the appropriate forum for asking
support questions. Your problem is not the result of a bug.
For a list of more appropriate places to ask for help using MySQL
products, please visit http://www.mysql.com/support/

Thank you for your interest in MySQL.

In the beginning, this was an RFE for more documentation. I hope, the next qualifies to be a useful piece that could go into the documentation:

From Gerrit P. Haase [gerrit@familiehaase.de], the latest binary mysql client executables and client library (static library only) separatly now (1.8 MB) can be obtained at:
http://anfaenger.de/cygwin/mysql/mysql-client-3.23.43-pc-cygwin-i586.tar.bz2 

gerrit.haase@convey.de

There is also as per "show variables": 
| have_crypt    | NO
...
| have_openssl  | NO
...

However, it appears that they cannot be set:
set GLOBAL have_crypt=YES
Unknown system variable 'have_crypt'

Under linux, have_crypt is YES

Gerrit has been able to compile a win32-nonCygwin version of mysqld that has a working "encrypt()" function - at least kind of working:
- we are not sure that it handles the salt properly
- the output is not compatible with the output of the linux version
But it correctly responds to the password verification requests. Thus programs doing password check will work both under linux and win32.

Here is how he did it:
<<In the config.h (the win32 version) change:
#undef HAVE_CRYPT
to
define HAVE_CRYPT 1

from the cygwin crypt package, take encrypt.h and encrypt.c, put encrypt.h in the'include' folder as crypt.h, enrcypt.c in the 'sql' folder (and if needed also in the "libmysqld" folder). In VisualC++ put encrypt.c in the corresponding project and then compile it.

Delete '#include <_ansi.h>' from (en)crypt.h and change the lines:

void _EXFUN(encrypt, (char *block, int edflag));
void _EXFUN(setkey, (char *key));
char * _EXFUN(crypt, (const char *key, const char *salt));

to:

void encrypt (char *block, int edflag);
void setkey (char *key);
char * crypt (const char *key, const char *salt);
>>

Two findings:
1) Gerrit's windows version creates shorter entries into the password table:
  $1gywq6R87ibc
and not something like
  $1$bdfb1bad$1VuRKjCl.BHl/JXAkx0YE/
as per my July 3 comment.
2) also the mysql-provided linux version is working fine with the short password table entries (probably at the  cost of the password not really being salted!)!

see also: http://bugs.mysql.com/1607

also just for the record: use this approach ONLY with prepared-statements, otherwise,

select encrypt( '$1', password) = password from TBL_USER where
login='ameyer'

where $1 will be replaced with the user provided password can be misused with the following SQL-Attack:
User-input = "wrongPw',password) = password || FIND_IN_SET('$"

For those who want this equally simple, but independent of the dbms in pure Java, see the "j-gnu-crypt-extension" package on https://sourceforge.net/projects/privasphere/

see also http://bugs.mysql.com/bug.php?id=15086 for using a similar mechanism for AES initialization vectors.