The Swiftype WordPress plugin will index all registered post types that are not excluded from search.
Typically, this means they have been registered with the public flag set to true (as this is a shortcut for exclude_from_search being set to false) but it is possible to register a private post type that is included in search. See get_post_types for details.
The default WordPress post types that are public are page, post, and attachment.
Additionally, an individual post must have a post_status of publish to be indexed. Attachments have a post_status of inherit and so are not indexed even though they are public.