One liner:
read -s -p "Password: " password
Under Linux (and cygwin) this form works in bash and sh. It may not be standard Unix sh, though.
For more info and options, in bash, type "help read".
$ help read
read: read [-ers] [-a array] [-d delim] [-i text] [-n nchars] [-N nchars] [-p prompt] [-t timeout] [-u fd] [name ...]
Read a line from the standard input and split it into fields.
...
-p prompt output the string PROMPT without a trailing newline before
attempting to read
...
-s do not echo input coming from a terminal