(Please note that these plug-ins are for self-hosted Wordpress installations, not those hosted on Wordpress.com).
The first thing to realise about plug-ins for Wordpress is that they can slow your blog down big time, especially if they load other code or pictures from other servers. That's why I don't use any of the really fancy ones, and I'd recommend everybody to take it easy with the amount of plug-ins you activate on your blog, but I understand that it's really tempting when you start your site!
1. Askimet. If you haven't got this plug-in activated, go to your dashboard and do it now. Askimet offers an excellent anti-spam commenting system that allow your visitors to have their say without slowing them down with hard to read "captchas" and prompts.
2. All In One SEO Pack. Easily add titles, descriptions and tags (although tags aren't really needed), and Search-Engine friendly URLS. If you want Google to love your Wordpress Blog even more, install this plug-in.
3. Contact Form ][. A simple, quick plug-in to add a contact form (rather than a comment form) anywhere on your blog. Good for "Contact Me" pages.
4. Google XML Sitemaps. If you want Google, and other search-engines, to search your blog faster and more regularly, you need a site-map. Working with your Google Webmaster Tools account, this plug-in generates a new site-map every time you add a new post or page.
6. Wordpress Automatic Upgrade. Like any piece of Software, Wordpress is being continually improved, and sometimes patched against security vulnerabilities. This plug-in makes upgrading your instalation a breeze.
7. WordPress Database Backup. If someone hacks into your site, or your hosts server fails, what's going to happen to all your content if you haven't backed it up? This plug-in emails you an archive back-up copy of your Wordpress database automatically, removing that worry.
8. WP-Cumulus. OK, I guess this is a bit of a flash (pun intended!) plug-in. It turns a boring tag-cloud into an animated wonder.
9. WP Security Scan. Check the security of your Wordpress Blog with this plug-in. Only the paranoid survive!
10. WP Super Cache. If Askimet is The Daddy, WP Supercache is the Mummy that keeps your Blog running nicely - basically it turns your potentially slow-loading dynamic CMS site into a quick-loading static HTML site. Great for any webmaster like me, who's using cheap hosting that isn't the fastest...