If I have a site (e.g. foo.com) and on the home page of foo.com, there is an image request where the src=bar.com..., will the cookies on the bar.com domain be sent to the ba
The cookie will typically be included in any type of request, but the scenario you describe is what's known as a third-party cookie (that is, the cookie is set on a domain that is different than the domain of the loaded page) and most browsers offer a privacy setting to block third-party cookies.
A third-party cookie allows the owners of bar.com to place an image (say a banner ad) on foo.com and track the users of foo.com even though those users have never visited bar.com. This is a privacy concern and many users elect to block such cookies.