As far as I know Ubuntu does not have a built-in reminder application. Surely there are some third-party applications that do the job well, but I didn't want to install extra packages etc.
So, I tried to build mine!

This reminder is based on at(1) command, that allows you to run a command at specified time.
In case it has not been installed on your system, just install it via:

sudo apt-get install at
at reads commands from standard input, so it is handy in case where we need an one-liner. For example the above command
echo "firefox" | at now + 1 minute
starts Firefox after one minute. You can find more examples in the following link.

So, we found a way to schedule one-time jobs but how are going to be notified?
notify-send to the rescue. This simple program sends notifications to the user via command line. For example the following

notify-send "Hello World"

shows this notification on the desktop!
Notifications are fully customizable: You can set summary, body or add an image to your notification. Just man notify-send for more information.

So with these two pieces, we can create the following bash function and incorporate it on our .bashrc file:

function notifymeat() { 
  echo 'notify-send -i /path/to/image.png "Impossible Mission robot" ' "\"$2\"" | at $1

If we run the following
notifymeat "now +1 minute" "Hello World"

this notification will appear on your screen

The name as well as the image of the pop-up window are from the infamous "Impossible Mission" game in Commodore 64.