When my Amazon colleagues first introduced a carousel implementation as an optional widget about 5 years ago, I believe they were wildly successful in A/B testing for a period of time; then we went through every page having about 6 of the damned things, then they basically disappeared... With enough users, sometimes A/B tests can degrade to novelty detectors.

You can only answer this question if you clearly know what success looks like for your site. Most folks will default to web stats like click-through rate on the carousel elements, but that is not always the right metric! Not everything on a site is intended to be high-volume navigation.

I work in the nonprofit space and we sometimes need to show that a certain topic is "important" to us, to help deliver on a fundraising or policy goal. Carousels are great for this, even though I know in advance that few people will click through. This success would be measured by directly checking with the desired stakeholders.

Another use for carousels is if you want your homepage to communicate an emotional tone--as opposed to enabling a task. A carousel of big, vibrant images can deliver an emotional message almost as well as a short video, but with a much lighter implementation. This success would have to be measured via user surveys or focus groups.

There's this study of the carousel on Notre Dame's home page

http://weedygarden.net/2013/01/carousel-stats/

Seems head honchos of marketing depts love these things because it satisfies inner politics of putting important stuff on the home page.

Ones that present data in order, like chronologically, and don't auto-scroll, leaving manual control to the user, work okay. Like "related products" on some websites, where the most relevant ones are first, but you might find something more interesting to you if you click a few pages in.