I use a variety of cameras for astrophotography, but they all have one thing in common: a mechanical shutter. While there are plenty of good 35mm and medium-format SLR cameras on the market, the number available with mechanical shutters is somewhat limited. Unless you like to buy batteries all the time, or don't mind limiting exposures to a few minutes, your astrophotography camera needs a shutter that can be held open indefinitely with a cable release, and that's what mechanically operated shutters can do. For this reason, most astrophotographers use older model cameras from Olympus, Nikon, Pentax, and others. Although I use other cameras as well, I've settled on Nikon as my choice for the bulk of my work, since they offer the largest selection of manual-focus lenses of anybody, and still offer several manual/mechanical 35mm SLR cameras as new items in their product line.
Some other features that come in handy for astrophotography:
Interchangeable focusing screens - matte, bright, non-prism screens are the easiest to focus on astronomical targets with
Interchangeable viewfinders - especially if a right-angle model is available
Mirror lock-up - to avoid vibrations ruining the shot when the shutter is tripped
For these reasons, I use the following:
Nikon F3HP - This is a heavyweight camera made famous by legions of photojournalists, and still available new (for now). It's also widely available on the used market, where a considerable discount can be had on it's high retail price. The F3 has all of the desirable features for astrophotography, along with multiple exposure capability, an auxiliary shutter release lever, and even an auto exposure setting for daylight or lunar photography. This is one camera that can meet just about any astrophotographic need, and is built to last a lifetime. Highly recommended.
Nikon FM2n - Much less complex than the F3, this fine camera therefore costs a great deal less as well. It features interchangeable screens, a self-timer, multiple exposure capability, and is very rugged and simple. The batteries only run the meter, and can be removed entirely for astrophotography. The lack of an interchangeable viewfinder is no problem with a Newtonian-style scope like the Epsilon. A right-angle attachment is available from Nikon, but it gives a dim, pinched view and is not really useful for anything other than some daylight purposes. Available new or used, and highly recommended.
Nikon FM10 - This Nikon isn't really a Nikon. It's made by Cosina, and badged as Nikon, or Olympus (the OM-10), and others. It's inexpensive and reasonably well made, but not nearly as rugged as the F3 or FM2n. It doesn't have interchangeable screens, so I don't use it for shots requiring critical focus at long focal lengths, but it does fit all my Nikkor lenses. The batteries only run the meter, and you should take them out for astrophotography, since the mirror lockup time is so slow on this camera when used on the bulb setting that the red LED (indicating underexposure - remember, it's dark outside at night!) can fog the film when the shutter opens. I use this camera a lot for star trails, and take it on vacation, since it's not a great loss if it's destroyed or stolen.
Pentax K-1000 - I only use this camera for star trails shots nowadays, but it's a great old camera, despite having no astrophotography features other than a mechanical shutter. Since the meter is of the "match needle" type and not an LED, you can leave the batteries in at all times. Sadly, this wonderful manual camera is only available used, having been discontinued by Pentax several years ago. Although other cameras are better suited to astrophotography, I still recommend getting one of these just because it's such a joy to use.
Fuji GSW 690-III - This is a fixed-lens, 6x9cm medium format rangefinder camera with a mechanical lens shutter. I bought it to get into medium format photography at a reasonable cost. The 65mm f/5.6 lens is the equivalent of 28mm in 35mm format, and I use it for star trails shots. Man, is it cool to get such huge slides back from the lab! The rangefinder focusing is no handicap for star trails, since the lens is so short you only need set it to infinity and trip the shutter. I'm having a lot of fun with this camera.
Fuji GW690-III - This is the same camera as above, but with a 90mm f/3.5 fixed lens. It's equivalent to a 37.7mm lens in 35mm format. I've used this for both star trails and deep sky work, and it works great. The faster lens means that I can stop it down to close to the same speed as the Borg 100ED and get sharp stars while matching exposure times when piggybacking.
Pentax 6x7 - Purchased in "Bargain" condition from KEH.com, I got this camera because it is the standard for medium format astrophotography. I've only just started using it, so I can't comment on it much, except to say that the first few piggyback shots using the Pentax 200mm f/4 lens look great on the light box. Update: I now have two of these, and shoot them every time out. What fun it is to produce huge 6x7 slides and negatives with these rugged cameras.
Focusing on all my cameras is now accomplished with a Mitsuboshi knife-edge focuser, one for 35mm and one for 6x7. These focusers, available from Hutech, are camera-specific, so I've got them calibrated to the Pentax 67 cameras and the Nikon F3HP. These things work like a champ, and deliver perfect focus every single time. No more wasted shots due to bad focus!