How to make Unity remember brightness settings?

The short answer is: you can't. Gnome power manager doesn't save the brightness setting. The best you can do is to automatically set it to a reasonable default at startup.

For 11.10, the only solution I have found that works is the one given here: http://blog.ishans.info/2011/09/25/set-brightness-automatically-at-the-startup-in-linux/

Save http://ishans.info/attachments/article/65/setBrightness.py locally, change the brightness percentage in the last line to your preferred value, and add a new startup application to run:

python /wherever-you-saved-the-script/setBrightness.py

I haven't found a way to get Ubuntu (I'm currently using 13.04) to save the last used brightness settings, but the default brightness of 100% on my laptop was too bright, and forced me to find a workaround (using the link denrossalenga provided).

Just add a line like this to your /etc/rc.local file:

echo 60 > /sys/class/backlight/acpi_video0/brightness

This will give you a startup brightness of 60%. Change as appropriate.