Latests Post Per Category

I looked all over the forum (as far as I can tell) and I read through the template help for specific tags, but I couldn’t really solve the problem I’m having.

My blog is hosted at http://www.dacrarealty.com/news/ What I’m trying to do is that on the right-hand side, the categories should show the titles of the last three posts (including links to those posts).

The only thing that I came up with is a plug-in, but it doesn’t really do exactly what I wanted. Is this something that can be done with the existing WP tags? Can anyone point me to some of the ones I should be looking at?