I'm accustomed to the "mail" command line program, but it is neither installed nor available in OpenWRT. Doing some digging with opkg and grep, I found a program called ssmtp that seems to do the job.
Installed ssmtp with the usual "opkg install ssmtp", and a little further digging led to finding the configuration file in /etc/ssmtp/ssmtp.conf. In my case, my ISP didn't require any security, so I simply set the "mailhub" option to my ISP's SMTP's server.
However, sending a test email to myself threw up the following error:
root@openwrt:/etc/ssmtp# echo test | ssmtp -s "test" email@example.com
ssmtp: 553 #5.5.4 Domain required for sender address
I guess my ISP's mail server insists on the sender domain being filled in, so I also set the "rewritedomain" option. (I also set the "hostname" option.)
Lastly, to accomplish my aim of sending an email to update me when OpenWRT reboots, I added the following line to "/etc/rc.local".
echo "Subject:`hostname` booted at `date -Iminutes | sed -e 's/T/ /' | sed -e 's/+.*//'`" | ssmtp firstname.lastname@example.org
The results are good enough for me. I now receive an empty email with a subject line in the form of "hostname booted at 2010-10-01 10:59" whenever OpenWRT reboots.
Now to the much more complicated task of figuring out if transmission/screen/top or some other background process is causing the spontaneous reboots. :(