WordPress is a secure website CMS and blogging platform. WordPress releases regular updates to fix any loopholes. In order to stay secure you should always update to the latest version of the software (including plugins).
Usefull Security Plugins:
This plugin allows you to create custom URLs for logging in, logging out, administration and registering for your WordPress blog. Instead of advertising your login url on your homepage, you can create a url of your choice that can be easier to remember than wp-login.php, for example you could set your login url to http://www.myblog.com/login for an easy way to login to your website.
You could also enable “Stealth Mode” which will prevent users from being able to access ‘wp-login.php’ directly. You can then set your login url to something more cryptic. This won’t secure your website perfectly, but if someone does manage to crack your password, it can make it difficult for them to find where to actually login. This also prevents any bots that are used for malicious intents from accessing your wp-login.php file and attempting to break in
WordPress File Monitor
Monitors your WordPress installation for added/deleted/changed files. When a change is detected an email alert can be sent to a specified address.
Login LockDown records the IP address and timestamp of every failed login attempt. If more than a certain number of attempts are detected within a short period of time from the same IP range, then the login function is disabled for all requests from that range. This helps to prevent brute force password discovery. Currently the plugin defaults to a 1 hour lock out of an IP block after 3 failed login attempts within 5 minutes. This can be modified via the Options panel. Admisitrators can release locked out IP ranges manually from the panel.
You can schedule backups hourly, daily, weekly amd have them send your email or save in a folder on the server. You MUST save backups.