How to deal with someone trying to login as admin?
These kinds of probes are very common across the internet. There are a few things you can potentially do to block this problem and reduce the success of an attacker.

First, I recommend everyone use Two Factor Authentication so that even if the attacker guesses your username and password they still can't login. There was a bounty for $500 to break TFA and although the white-hat attackers had username and password they couldn't break in.

The security review module or Droptor can help monitor these failed logins. If they happen a lot then you need to start taking more actions. Brute force attacks on passwords only work if someone does them a lot so if it just happens a few dozen times I wouldn't worry.

You can track the IP address in use by this person using watchdog entries and then use the built-in D6 Access Rules (or the d7 equivalent - http://drupal.org/project/user_restrictions ) to block access via that IP. You could also deny access to the IP in Apache or some other server level firewall. The firewall/webserver is a more efficient place to block the users in terms of load on the server, but it usually requires a bit more effort.

For Drupal 6 and 7, AjitS has provided an answer with a good description of how to use a rate-limiting feature to prevent repeated login attempts from the same IP.