1. Telescope mounts (stability)  
To a large extent, a telescope is only as good as its tripod and mounting. A telescope magnifies everything, including vibration. That's why many telescopes with decent optics are rendered useless when supplied on a cheaply made mount. The mount's adjustments should be smooth, yet precise, as you'll be using them to track the slow and steady apparent movement of the stars. Smooth and precise movements (and a motor drive) are an absolute requirement for astrophotography.
A telescope mount has two functions- (1) provide a system for smooth controlled movement to point and guide the instrument, and (2) support the telescope firmly so that you can view and photograph objects without having the image disturbed by movement.
There are two major types of mounts for astronomical telescopes:

(1) Altazimuth -- the simplest type of mount with two motions, altitude (up and down/vertical) and azimuth (side-to-side/horizontal). Good altazimuth mounts will have slow-motion knobs to make precise adjustments, which aid in keeping tracking motion smooth. These type mounts are good for terrestrial observing and for scanning the sky at lower power but are not for deep sky photography. Certain altazimuth mounts are now computer driven and allow a telescope to track the sky accurately enough for visual use but not for long exposure photography.
(2) Equatorial -- superior to non-computerized altazimuth mounts for astronomical observing over long periods of time and absolutely necessary for astrophotography. As the earth rotates around its axis, the stationary stars appear to move across the sky. If you are observing them using an altazimuth mount, they will quickly float out of view in both axes. A telescope on an equatorial mount can be aimed at a celestial object and easily guided either by manual slow-motion controls or by an electric clock drive to follow the object easily across the sky and keep it in the view of the telescope. The equatorial mount is rotated on one axis (polar/right ascension) adjusted to your latitude and that axis is aligned to make it parallel to the Earth's axis, so that if that axis is turned at the same rate of speed as the Earth, but in the opposite direction, objects will appear to sit still when viewed through the telescope.
There are two basic types of equatorial mounts:
(a) German Mount -- both Newtonian and refractor telescopes normally use this type mount. A large counterweight extending on the opposite side of the optical tube is its distinguishing feature. The counterweight is needed to balance the weight of the optical tube.
(b) Fork Mount -- most catadioptric and other shorter optical tubes use this style mount which is generally more convenient to use than the German mount, especially for astrophotography. A more recent state-of-the-art computer controlled telescope allows fully automatic operation making it extremely fun and easy to locate objects while saving the observer considerable time and effort.
Unless the telescope is a tabletop model, it should be set on a tripod or pier-type platform. These must be rigid and minimize vibration. They should be portable and lightweight as well as easy to handle and set up. Appearance can be deceiving, as bulk and weight are not as important as a well engineered tripod or pier.

2. Wedge

A wedge is usually used with a fork mount to tilt your telescope up to the celestial pole, at an angle equal to your latitude so that a clock drive may function properly and the setting circles give accurate readings. The wedge is mounted between the bottom of the fork mount and the tripod.

3. Clock motor drive 

An electrical system of motors and gears utilized with an equatorial mount. It compensates for the Earth's rotation during astronomical usage keeping celestial objects centered in the field of view.

A clock drive is essential to do astrophotography. The electrical system can be AC or DC depending on the type of system used. The gearing system is usually a spur gear or a worm gear type, both of which can be good if manufactured properly.

4. Setting circles 

Dials for right ascension and declination that allow you to locate celestial objects easily from their coordinates as listed in star charts. For setting circles to work effectively, the telescope must be equatorially mounted and polar aligned.

Digital setting circles allow you to computerize your telescope. They have thousands of objects in their databases and allow you to see numerous objects in an evening.

5. Finderscope

A small auxiliary telescope with crosshairs attached to the main telescope. It is of low power with a wide field of view and assists you in pointing to find objects to observe through the main telescope. Most finderscopes give an upside down and left/right reversed image.

6. Star diagonal

With some telescope designs the viewing position of your eye is in an awkward position when observing overhead. A star diagonal (a prism or mirror set at a 90 degree angle to the telescope tube) is designed to make viewing of the sky more convenient and comfortable and swivels right and left as required. Newtonian-type telescopes do not need a star diagonal since the eyepiece is normally in a comfortable viewing position already.

7. Eyepieces (ocular)

An eyepiece is simply a precision magnifier. The eyepiece used with a telescope magnifies the image that is formed by the main optical system. There are many different kinds of eyepiece designs for various applications. The design and quality of the eyepiece can drastically affect the overall performance of the telescope system. Common barrel diameters are .96", 1?" and 2".

8. Accessories 

Barlow Lenses, Eyepiece Filters, Motor Drives, T-Adapters, Dec. Motors, Guiders, LPR Filters, Tele-Extenders, Solar Filters are the names of a few accessories in an enormous offering of accessories for telescopes. As your interests expand, accessories are available to help you achieve maximum satisfaction.