I'll start with a few less famous ones that I think should be used by everyone.
- Broken Link Checker - Does exactly what the name suggests. It automatically checks every link you've got in every post to see if it no longer works, and notifies you if that's the case so you can fix it.
- Limit Login Attempts - This is one I never thought I'd really need, but installed anyway out of paranoia. Now I'm really glad, because it seems like every few days someone tries to guess my passwords. This plugin will send you an email letting you know when it bans an IP that tried to login to your Wordpress install.
- WP Security Scan - An automatic security scanner that will send you an email when it finds alterations made on your site or anything else suspicous. Of course there are false alerts caused by things like software updates, but usually the plugin marks those as low or medium priority. Anything marked high priority is what you need to pay attention to.
- Tynt Insight for Wordpress - This is a very interesting plugin that I'd never have thought to search for and wouldn't have installed if it hadn't been recommend to me. Tynt Insight will do several things for you: it'll let you know when someone copies text off your site, it'll create links back to your content if someone copies enough text off your site, and it'll let you know what search terms drove traffic to your site. I'm definitely installing this on every new Wordpress site I setup.
- Wordpress Backup to Dropbox - I wrote a post about getting more free Dropbox space, and mentioned this plugin there. I've found it to be great for my peace of mind, since it gives me a complete site backup that gets synced across everything I've got a Dropbox client installed on. The current version seems to need an update to work correctly with the latest Wordpress release.
And here are a few more plguins that I like a lot and have seen recommended in other Wordpress plugin lists.
- Ad Injection - A great way to add Adsense or other ads to your site. You can mess with a lot of different options to do things like place ads in random parts of a long post, and align them to the right edge of the post with the post text wrapped around it. It makes ad blocks look a lot more like what you see on big sites. You can set different ads in different parts of your posts, limit advertising to only certain kinds of posts and keep them off the homepage, and easily swap out ad codes without having to edit every page on your site. If you're going to try making money with ads, use this or something like it.
- All in One SEO Pack - A really popular one, it helps make it easier for Google and the other search engines to understand what your site is about so they can figure out if they should display it when people search for terms related to your content.
- Google Analyticator - If you're using Google Analytics to track your site traffic, and you should be, this will give you a quick overview of your site stats right in your Wordpress admin main page, in addition to adding the Analytics tracking code to your site for you.
- Google XML Sitemaps - This will help notify Google when you add new posts or pages to your site.
- Nofollow Reciprocity - This is plugin is an interesting concept. It's supposed to help small websites compete against the big ones like Wikipedia in search engines by setting the outbound links on sites which use the plugin and point to Wikipedia or other big sites which use nofollow links to be nofollow too. This will only work well if a lot of sites start using the plugin though, but it's still useful to some degree for preserving PageRank on your site, for whatever PageRank is worth these days.
- W3 Total Cache - A caching plugin to speed up your site and reduce load on your webhost. There are a lot that do this job, this is just the one I use and have seen recommended the most.
- Yet Another Related Posts Plugin - This is an automatic way to link to related posts on your site at the end of every post you've got. This both helps search engines understand your content, and helps people reading your site stick around longer and read more.