When your computer is shut down (or the cron daemon is otherwise not running), cron jobs will not be started.
If you have jobs that you would like to run after the fact during those times when the computer is shut down, use anacron. Installed by default, see "man anacron", "man anacrontab", or the file /etc/anacrontab for more info.
Ubuntu uses anacron by default for crontab entries in:
/etc/cron.daily
/etc/cron.weekly
/etc/cron.monthly
leaving the remaining crontabs to be handled by the main cron daemon, specifically:
/etc/crontab
/etc/cron.d
/var/spool/cron
NOTES
Anacron itself does not run as a daemon, but relies on system startup scripts and cron itself to run.
On the Ubuntu 8.04 box I'm looking at, /etc/init.d/anacron is run at boot, and again by cron each morning at 07:30.
The README at /usr/share/doc/anacron/README.gz has a slight bit more info than is contained in the manpages.
EXAMPLES
For simple "daily", "weekly", "monthly" jobs, put a copy of or a symlink to the script in one of the /etc/cron.{daily|weekly|monthly} directories above. Anacron will take care of running it daily/weekly/monthly, and if your computer is off on the day the "weekly" scripts would normally run, it'll run them the next time the computer is on.
As another example, assuming you have a script here: /usr/local/sbin/maint.sh
And you wish to run it every three days, the standard entry in /etc/crontab would look like this:
# m h dom mon dow user command
0 0 */3 * * root /usr/local/sbin/maint.sh
If your computer was not on at 00:00 on the 3rd of the month, the job would not run until the 6th.
To have the job instead run on the 4th when the computer is off and "misses" the run on the 3rd, you'd use this in /etc/anacrontab (don't forget to remove the line from /etc/crontab):
# period delay job-identifier command
3 5 maint-job /usr/local/sbin/maint.sh
The "delay" of "5" above means that anacron will wait for 5 minutes before it runs this job. The idea is to prevent anacron from firing things off immediately at boot time.