As the title states I am curious if there is a way to run malware, spyware, and general virus threat assessments against a website. Or any other ways to see if a website(s) is safe.
If you are looking for the public facing side of any site Securi http://sitecheck.sucuri.net/ does a pretty good job. If it's your own WordPress site I would recommend Wordfence. An additional check for WordPress is https://wordpress.org/plugins/gotmls/
If you own a website/ Blog then following are available:- 1) GeoTrust Anti Malware Scanner 2) SiteLock 3) Godaddy Web Scanner 4) COMODO Web Inspector. These will help you to know the malware and other status, will also help in removal & will give you web seal to display too.