In my most recent WordPress installations, these are the plugins I install first:
1) Acunetix WP Security: all sorts of changes in settings and file checks to increase security
2) Limit Login Attempts: Straight-forward plugin that blocks brute-force bots
3) Simple Login Log: exactly what you imagine ;)
4) Google Analyticator: adds GA tags on your page and also can bring GA statistics in your WP dashboard
5) NGFB Open Graph+: Manage your Open Graph tags for Facebook (there is a pro version with also Twitter support)
6) WP Super Cache: Caches your pages to increase speed. I tend to prefer it over W3 Total Cache
7) Visual Composer: This one isn’t free, but for 25$ you can give your clients a powerful visual editor to create complex page layouts
So what are your can’t-live-without plugins? :)