While carousels are traditionally seen as a good way to squeeze more content into a limited amount of screen space, studies (see Should I Use a Carousel?) show that site visitors are most likely to ignore anything beyond the first slide, and a poorly built carousel can irritate users, leaving them with negative feelings towards your site and your organization.
From an accessibility standpoint, it is possible to build an accessible carousel, but this usually has to be done from scratch, as most popular carousel widgets (e.g. Flexslider) have been unwilling or unable to update their code to make it properly accessible. If you are interested in building your own carousel system, the AccessIQ tutorial and W3C tutorial will give you a good framework to help you code your system properly.
So, in short, for the time being it's best to avoid carousels whenever possible, especially with Drupal sites, as there is yet to be a really simple, easy to configure carousel system for Drupal.