Almost all of the testing I’ve managed has proven that content delivered via carousels are missed by most users. Few interact with them and many comment that they look like adverts — we’ve witnessed the banner blindness concept in full effect.
In terms of space saving and content promotion, a lot of competing messages get delivered in a single position that can lead to focus being lost.
Carousels are effective at being able to tell people in marketing/senior management that their latest idea is now on the home page.
They are next to useless for users and often “skipped” because they look like advertisements. Hence they are a good technique for getting useless information on a home page (see first sentence of this post).
In summary, use them to put content that users will ignore on your home page. Or, if you prefer, don’t use them. Ever.
By the way, these views are not my own, but are based upon observing thousands of tests with users.
As a user I find carousels faintly annoying:
Most have usability fail which I fall into the categories described in this article:
5 Big Usability Mistakes Designers Make on Carousels
No ability to bookmark a particular item on the carousel, for example take a look at the BBC News photo carousel they use: http://www.bbc.co.uk/news/world-africa-14619799 There’s no way for me to bookmark the sixth item and send a link.
Carousels that don’t allow me to right click on an item and “open in new tab/page” – flash carousels
Carousels that have unpredictable non-intuitive navigation such as rotating content for no good reason just because you moved your mouse over it.