SSH hangs on login after 'last update'

This is usually because one of the files used by login has some function that takes a long time to return. It will commonly be either in your own home directory, where you should look at

 .profile
 .bashrc
 .login
 .kshrc
 .tcshrc

If it's none of those, look in /etc for the same files, but usually without the dot:

/etc/profile
/etc/bashrc

and so on. The culprit will often be something that does a DNS lookup, but it might also be that you have it set to check when you last logged on, and your utmp/wtmp/btmp is very large.

ls -lhS /var/log/