Yes, it's safe.
If you refer to privacy, consider making your blog closed to a smaller number of users at Settings > Privacy.
HALFSPIRAL: It's has safe as at least any other on-line software. WordPress work really hard to fix any discovered bugs / vulnerabilities found. There have been security issues in the past, particularly SPAM commenting. So make sure you have your comments set for approval so you can filter the idiots who want to spoil your Blog.
So if you use WordPress always install the latest updates or version (they are quite frequent) but the good news is that version 2.8+ now has an auto-update feature which makes life a lot easier !!
WordPress is Fun and very reliable.
Now wordpress just released the 3.0, it's more perfect security.
Yes Wordpress is safe. Checkout operture.com for plugins that will make your Wordpress more secure!
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