Contrary to popular belief, Jetpack does not require you to connect your website to WordPress.com before you can use it at all.
Several Jetpack modules are self-contained and do not require a WordPress.com connection to function:
The Development Mode for Jetpack plugin enables (wait for it…) Jetpack Development Mode, which does two things:
It also means you can stop using individual Jetpack modules that have been forked out into standalone plugins by random people. These plugins tend to be unsupported and out of step with the latest version of the official Jetpack equivalent.
Please note that this plugin requires Jetpack to be activated alongside it to be of any use, and will not help with the following modules that do require a WordPress.com connection:
Lists of Jetpack modules in this plugin description should not be considered comprehensive or authoritative, and may change at any time.
Tiled Galleries requires the WordPress.com Photon CDN; however, in Development Mode, Jetpack provides a fallback so developers can have a similar experience during development and testing.
Other modules may also have “reduced functionality” but retain “a good-faith representation of the feature.”