I often get asked whether it's better to shoot a single image or multiple images stacked together to create a star trail. The answer to this question depends on several circumstances which I will go into in detail below. Personally, I use both methods, as they both have their pros and cons under different circumstances.
Single Image Star Trail
This method of star trails involves taking a single image, usually between 15-45 minutes, followed by a second dark frame image of the same period of time as the initial trail image. The dark frame subtracts any hot pixels caused by your sensor getting warm, which introduces a large amount of noise into the image.
This can either be done by taking the same image just with the lens cap on or by turning on long exposure noise reduction (LENR) in your camera settings. I usually use the LENR option as it is done automatically in camera and subtracts it directly from the image, allowing you to see the end result once it has completed the image. However, if you plan on doing several images for the same length of time, then a separate dark frame is a better option as the same dark frame can be used for several images, saving time in the long run.
It is important to note, however, that a separate dark frame is required for every different time period used for star trails (i.e. a 15 minute exposure needs a 15 minute dark frame and a 30 minute exposure requires its own 30 minute dark frame).
The dark frame being the same length as the single star trail image is one of the biggest cons of this method and is why a lot of astrophotographers prefer the multiple exposure method over a single image.
What I like most about this method is that you can see the end result in camera after it has completed and decide if you need to take another image or adjust your composition for a better image. In addition, exposing for such a long period of time allows you to increase your depth of field by changing your aperture (i.e. going from f2.8 to f4 or f5.6). This is great if you are very close to your foreground and require a greater depth of field to keep everything in focus.
The second pro of this method is that more ambient light is picked up onto your sensor, especially from the foreground. This means that when editing your image in post-production, you can normally recover a lot more detail from your foreground. This being said though, a separate image can be shot for the foreground and blended in for both methods, so this shouldn't be a primary reason for using this method and should be thought of more as a secondary advantage.
The last pro for this method—and the reason I still use this method—is that it's great if you want a short star trail for a particular location and have multiple locations you wish to shoot at. What I mean by this is that you can take a 20 minute image then walk to your second location while the camera takes the dark frame image and normally by the time you've reached your second location, the LENR has completed the dark frame and you'll be ready to take your next photo.
Unfortunately, the cons are numerous for this method and you need to weigh up the various factors before deciding on your preferred method.
The worst cons of this method, other then having to wait for the dark frame, is the length of time the single image takes and the fact that any interference means all that time required to take the image will be wasted. So if you are shooting on a windy evening then any motion introduced during the single exposure will be picked up, any clouds that move across the sky will affect your image, and—worst of all—any light pollution introduced into your image could completely ruin it. This could be from a fellow photographer's headlamp or a passing car or hiker's light. You will see when I discuss the multiple exposure method why this isn't an issue. Plane trails will also be picked up if a plane flies across your field of view, and this will have to be removed in post-production.
The last con often mentioned by photographers is that if you leave your sensor open for too long, it can overheat and become damaged. This is true, though it was more of an issue in the past with older cameras. Newer cameras have safety shut off sensors built in, and your camera should shut down before damage happens to your sensor, so this isn't a major concern nowadays. But I wouldn't advise using this method for images longer than an hour due to the heat build up of your sensor and triggering a shutdown, as well as the possibility of running out of battery life. So if you plan on doing a long star trail, I would advise using the multiple exposure method.
Multiple Image Star Trail
As the name implies, this method involves taking multiple images (usually 30 seconds long, as this is the max exposure time on most cameras without using bulb mode), which are stacked together in post-production using software such as Starstax (free) to create a star trail.
An intervalometer is required for this method. Most high-end DSLR cameras have this function built in, but if your camera doesn't then you can buy a separate intervalometer for your camera.
One advantage of this method is that only a single 30-second dark frame is required, which can be used across all your images to subtract any hot pixels, saving a lot of time compared to the single image method.
The reason I mention 30 seconds is because you want to have a very small star shift present in each image. This means you need to expose longer than your rule of 500 exposure time (see basic astrophotography tutorial - coming soon!). This small shift makes the completed image look more natural. Instead of blending dots (stars correctly exposed), it will be blending dashes (stars with slight shift), resulting in the final image trails looking smooth and concentric.
One of the biggest pros of this method is that these images can also be used to create a time-lapse video, so if you want to shoot a 4-6 hour time lapse of the night sky, you can use these same images to create a star trail. I like the flexibility of this as it gives you different options from the same images.
Another advantage to this method is that any interfering factors, such as light from your headlamp or a plane in the sky, can be removed. These individual frames that have been ruined can be excluded from the final star trail stack of images without losing your star trail.
One of the cons of this method is that it does require a bit more setup time with the intervalometer, but once you've done it a few times, it isn't really an issue. Another con is that, while not complicated to use Starstax (free tutorials are available on YouTube), this method does require more post-processing time. In addition, you can't see your final star trail in camera while out under the night sky, but this shouldn't be a major issue once you have done it several times.
I would say the biggest considerations when deciding which method to use are time and convenience. If you want a short trail (remember focal length affects trail length, so if you aren't shooting very wide 20-24mm, you can get really nice trails in a short period of time) of 15-20 minutes, I would use the single image method as long as there isn't much interfering light around. I would then use the multiple exposure method for longer trails or if I had a very wide angle lens and would run this for 1-3 hours depending on how much trail I want.
In the end, as with all photography tips and methods, it comes down to personal preference, but I hope I was able to give you some insight into my reasons and help you make up your mind on some issues you may have been struggling with.