I think it deepens largely on what the site is about and what needs the content aspect of it might call for. First thing I always do is install the security scripts, either iTheme or Wordfence. I also use a database optimizer, which I find helpful, gallery plugins and video plugins are next on the list. Sometimes, but more rarely these days, a stats plugin.

The lightbox style gallery plugins generally work well, but video plugins have given me a few problems over the year, I think largely due to conflicts with updates. I wrote my own embed script a couple of years back, still works today, but I tend to used the hosted embeds from my sponsors when they are available, however they’re not always the best either. The one I do like is the flow player WP plugins, seems very sound so far.

I’d love to hear more of what people are using, but again I think the decisions are predicated on what your site is and what the needs are based on the product or content.

I use:
Akismet (essential)
Ninja Firewall
One I wrote that handles SEO stuff and shortcodes that I use for things like video embeds
Enhanced Text Widget (only use it when I need PHP in sidebar widgets)

I highly recommend spending the time to learn to write your own plugins. It’s really not that hard and you know exactly what’s happening in the code on your site.

If you ever need to change a lot of links on your blog, this plugin makes it easy: Velvet Blues Update URLs.