In what use case is an Infinite Scrolling Website a good idea?

Infinite scrolling is a great idea for sites that deliver a huge amount of content in each section (like Facebook, Quora and 9gag, which indeed use infinite scrolling). Email providers like Yahoo and Gmail are also using it. It's pretty dandy to click on a menu item and plunge into the depths of a page (there is a lot of scope for animations and effects here), so it also finds wide use in informal sites, sites for startups and sites of web designers. It's cool if used right, though with all things cool it probably won't be cool in 6 months. It's not a great idea for formal business websites (I am not talking about startups). You can see that Google, LinkedIn and many top sites don't use it (or if so, only in small sub-sites like Gmail where it actually helps). A multi-page design appeals to users from Gen X, and that is who most top companies are targeting. Also, if you run a blog or a site with view of generating ad revenue and you don't have a huge user base, it's probably best to use a multiple page design for reasons that Sahil pointed out. I'd say it depends on these factors as well as what the client actually wants. They have the final say after all.