Can I install apps bought on the Mac App Store on multiple computers? If I buy an app on through the Mac App Store, can I install it on both of my Macs?

I use the same iTunes account on both of them.
Yes. Just run the App Store app on the second Mac and go to the Purchases tab. You'll see a list of the apps you've already purchased, with an Install button next to each one - click the button to install on the second Mac.