Basic Wordpress.org Security

I find that it's usually "from Russia with love"

I use and recommend iThemes Security plugin. Install the plugin and configure it. I would highly suggest you to atleast Fix all the High Priority items to maximize your site's security.

- Nizam

You can also use BulletProof Security plugin. The feature :
- .htaccess Website Security Protection (Firewalls)
- Login Security & Monitoring
- DB Backup: Full|Partial DB Backups | Manual|Scheduled DB Backups | Email Zip Backups | Cron - --- Delete Old Backups
- DB Backup Logging
- DB Table Prefix Changer
- Security Logging
- HTTP Error Logging
- FrontEnd|BackEnd Maintenance Mode
- UI Theme Skin Changer (3 Theme Skins)

Here are the Wordpress Security Plugins that I use:

Plugin #1 = http://wordpress.org/plugins/captcha/changelog/
Plugin #2 = http://wordpress.org/plugins/limit-login-attempts/
Plugin #3 = http://wordpress.org/plugins/better-wp-security/

That'll make your site pretty darn to break.

1) There are a few great security plugins

Like..

SiteGuardian
iThemes Security

2) Make sure you backup all your data, very frequently..
using FileZilla or another service

Besides just securing your wordpress installation, also make sure your server is secure as well, as if they get access to that it won't matter what you have installed onto wordpress. :p

Most exploits are the result of poorly engineered plugins. None of these security plugins are going to do much (if anything) to prevent that. If they have some features that you like, install it. Just don't let it give you a false sense of security. Keeping everything updated is the best line of defense.

Scan your new site for vulnerabilities, and check plug-ins against the US National Vulnerabilities database. That will close any "back doors".

Install Wordpress Firewall 2, Keep your Wordpress core and plugins updated. Dont use pirated themes. That's the basics. And there are lot many advanced things too.

Basic list - (some repetitive to other replies above)
1. Keep WP version and plugins up to date. That is the single most important thing you can do.
2. Be very careful when buying themes that have plugins integrated - many of these do not update the plugin portion when there is a security problem. Envato had to notify/take action with the Rev Slider breach a few months ago that included thousands of themes that were sold and had this plugin included.
3. Get a good host that works with a lot of WP installs. They are likely to make sure you are notified when there's a problem since shared hosting means that a lot of installs can be compromised by one bad apple.
4. You could try Sucuri, iThemes Security, those are two really popular companies that provide good support to their users.
5. Set up a few Google Alerts for WP security issues if you do not visit the WP forums or FB groups very often - that way you'll get a notification when there's a problem and you can make sure you're covered.
6. Log in and check for updates in your admin periodically. That means more than once every six months lol...
7. Most of the stuff in the repo has been checked and is decent. That doesn't mean it's all well written so keep in mind when you install plugins that you're putting your site at risk. Don't stop installing plugins, just be choosy.
8. If you're using cPanel, set up a backup at least once a week. Keep at least 3 copies of backups in case something got you and you need to revert. Depending on date of breach, you should have at least one good backup (maybe not if you backup every day, once a week is plenty). Keep a separate copy of your DB occasionally in case that's compromised. Once a month is probably enough unless you have a ton of new content.
9. If it looks too good to be true, you know the deal...