Can I run multiple blogs from my local machine

To achieve this simply, make sure your WordPress version is 3.0+. It is always recommended that you have the latest.

First you need to activate the network:
http://codex.wordpress.org/Create_A_Network

Note that, as you are using a local installation, you won’t have the choice to create your network in sub-directories as subdomains won’t work. By reading and following the information in the link above, you’ll get what I mean.