Hosted components for web sites and hosted services for web site owners. These don't require software to be downloaded or installed on a web server. The component or service must be hosted on the servers of the site providing the component or service. If the component or service is hosted on the web site owner's server or the web site owner's hosting company server then the site can not be listed in this category.
Some of these are intended only for the site owners, though most are intended for visitors to the site. In the case of the latter, the site owner usually just needs to link to the site or copy and paste some script or markup.
Services listed here can be pay, ad-supported, or free.