Migrating Users from Older Versions of Drupal
Are Drupal's password hashing mechanisms consistent across different versions?

No, D7 and D8 use SHA512 with a salt. Drupal 6 uses MD5 without a salt.

If not, are there tools to support migrating user accounts and converting the passwords between versions?

Yes you can just rehash them.

If a no to migrations, are there modules that provide a standard experience for this situation that allows an old user to pick a new password?

Yes there is a really simple way (one example is). Make sure you BACKUP before you do anything. If this does not work for you, google how to convert drupal 6 passwords to drupal 7. There is a ton of different ways.

&lt;?php
        require_once DRUPAL_ROOT . '/' . variable_get('password_inc', 'includes/password.inc');
        $res = db_query('select * from drupal.users');

        if($res) {
                foreach ($res as $result) {
                        $hashed_pass = user_hash_password($result-&gt;pass, 11);
                        if ($hashed_pass) {
                          $hashed_pass  = 'U' . $hashed_pass;
                          db_update('users')-&gt;fields(array('pass' =&gt; $hashed_pass))-&gt;condition('uid', $result-&gt;uid)-&gt;execute();
                        }
                }
        }