What are the most important links to have on a website to get a good quality score when buying AdWords? I am in the process of rebuilding my website and this is what I will be adding so far:

Contact Us
Privacy Policy
Terms and Conditions

What else does googlebot look for to increase quality scores?

I don't know if it affects your quality score, but I know googlebot likes to see a sitemap.xml and a robots.txt.

If you are selling products then a Returns Policy is important too. I'm not positive that it will impact quality score -- but it would make sense that it does.