Dammit! The title of your post got me all excited to use my witty answer "Yesterday in Kiev.":(

Now I have to give a real answer.

I think you want to know the last time it was used as weapon. So not counting Aircraft Catapults and what not.

The last large scale use of catapults as an instrument of war was in WWI, where they were used to propel hand grenades. Here is a video of the British using one kind and an image of french troops using another.

However use of catapults have continued to be made and used in smaller conflicts up to the present day. Last year videos were made of Syrian rebels using catapults and [trebuchets] (http://www.youtube.com/watch?v=WttMxBc0kS4) during the Syrian Civil War.

The catapult is a cheap and relatively simple weapon to make. It can propel rocks, grenades or homemade explosives. This is why we continue to see it's creation and use even in the modern age.

[Here] (http://www.dailymail.co.uk/news/article-2378815/The-Syrian-trebuchet-Rebel-fighters-resort-Roman-style-tactics-using-DIY-catapults-battle-Assad.html) is an article on their use in the Syrian Civil war.

[Here] (http://www.vlib.us/wwi/resources/springguncatapult.html) is some more information on the WWI catapults

Given that catapaults (as mechanical ballistic devices, not necessarily the medieval versions) have been used recently not only in Ukraine, but in Syria and along the Mexico-US border, I'm removing this question as it violates our 20 year rule.

As well the question is a little broad.