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Yes, it is possible to de-hash the passwords in /etc/shadow . There are programs (John the Ripper being the most-used on Unix) which can use dictionary and brute-force attacks against the hashes, and will eventually hit the right password.
Sorry, should have been a bit clearer. With exceptions of brutal force, database lookups etc, is there a way the user could use the encrypted password and send it to a ssh server for example? The password the user types in is encrypted with MD5 before sent to the ssh server isn't it? So a user could modify a SSH client potentially to send me string to the ssh server to get in as root?
SSH encrypts the whole stream and the password is passed down that encrypted channel, but it's not MD5 that's used (MD5 isn't an encryption algorithm, it's just a hash). The password (along with everything else) is decrypted by the SSH server before being used - most Linuxen use PAM to process authentication, so the password's passed to PAM in plaintext to be compared with the hash in /etc/shadow.
So no, having the MD5 hash on it's own won't let anyone in.