Telescope or astronomy devices control
There are nearly as many different astronomical set-ups as astronomers. Lots of devices are required in a set-up, and many of each type exist. Many are not supported by free software. A hardware compatibility list is being done here.
Acquisition software generally have to handle high-end cameras, DLSR and focusers. Autoguiding software generally have to handle low-end cameras and telescope motorisations, possibly focusers too. They make very different tasks and address a large range of devices.
Multiple functionality software
Telescope control: Autoguiding
See OpenPHD Guiding, GoQat, Ekos for KStars which is using lin_guider's code. Qastrocam-g2 also has a guiding capability. What else?
Telescope control: GoTo
GoTo functionality is generally managed by cartography software.
Image acquisition
The others has a list of software supporting each camera. Examples are GoQat for QSI cameras and Gphoto2 for DSLR.
INDI-compatible cameras can be used with Ekos.
cccd is a simple astronomical CCD controller. It supports TSNK-lab ICX285AL cameras, QHY5, QHY6, QHY9, QHY8L, DSI2PRO, DSLR.
Qastrocam-g2: capture and simple guiding software for astronomy, using V4L2 acquisition. It also supports QHY5 and QHY6 cameras in release 4.9.
XmCCD is a camera capturing tool for Apogee Alta and SBIG cameras, supporting their filter wheel, compatible with INDI. It displays captured images in DS9.
oaCapture is a recently created free software that features V4L2 capturing in a Qt application. It provides many image capture controls, can demosaic images and save them in SER files. Support for other cameras than V4L2 has been introduced (ZWO ASI, QHY5, QHY6, SX Lodestar, Atik ATK-16 and The Imaging Source), as well as filter wheels on Linux (Xagyl and Starlight Xpress) and it also works on Mac OS X.
Other devices
Filter wheels, focusers, domes and so on. The Hardware compatibility list lists the software supporting each devices. Multiple functionality software could handle them too.
Standardization initiatives and remote telescopes systems
Some projects do not focus only on one particular device or even type of device, and provide abstraction layers or even try to standardize the way astronomical programs communicate with each other and with devices. An example of such an abstraction layer would be the Ascom Initiative on Windows platforms.
INDI is such a project for all kinds of devices. It is getting very popular and many devices already have INDI support. Before developing INDI, the author, Elwood C. Downey of ClearSky Institute, developed Talon, another free software for automated observatories, which is still used in several observatories around the planet.
Another software for autonomous observatories, the Remote Telescope System (RTS2), also developed an abstract device layer, enabling control of all possible combinations of mounts, CCDs, photometers, roof and cupola controllers. It is also used in several observatories around the planet.
Unicap is a way to access imagery devices, it doesn't seem to be used by many or actively developed anymore.