There are many different types of cameras that can be used for filming, all with different strengths and weaknesses. There are 8 different types of ways to record movies, all which will be described in detail.
DSLR and mirrorless Cameras
DSLR cameras are one of the best, and cheapest, ways to shoot good video. With interchangeable lens, DSLR's provide a range of different angles, zooms and depth of fields. These cameras are extremely adjustable to most situations and are easy to transport, with little weight. DSLR's are good in low light, have good shallow focus effects and lots of creative control. Unfortunately, sound recording can be awkward, as can holding the camera. They also have some image quality problems in some situations and have a limited recording time. These are still excellent cameras and are extremely good for making creative short films on a tight budget.
Prosumer Camcorders
Prosumer Camcorders are the most common cameras used for filming higher budget films, documentaries and more. They give you more creative control and you'll get better results in low light. Most prosumer cameras also allow you to plug in separate microphones and headphones. These cameras have good image and sound quality, are fairly easy to use and have better handling than DSLR's. They do have some cons however. The are bigger and more complicated than basic camcorders, and image quality may not be as good as a system still cameras. For some, the image quality may not be accepted by broadcasters. This is only a problem for a few. These are excellent cameras but are more expensive than a DSLR.
Pro Camcorders
Professional camcorders allow the user to have a lot more control than basic or prosumer camcorders. These cameras can be difficult to learn however, as they don't have menus like the previous cameras, and have dials and buttons. This can work faster once you're used to the camera. They also can be upgraded as time goes on, allowing these to be an investment piece as well. Pro Camcorders have good image and sound quality, lots of creative control and are extremely fast once you know what you're doing. However, they are large and quite heavy, and can be fairly expensive. They take time to learn and the images may not be pleasing as those from cheaper system still cameras.
Interchangeable lens video cameras
Interchangeable lens video cameras are large and expensive. But they have the advantages of both pro camcorders and system still cameras. The provide excellent image quality, great sound and lots of creative control. They also handle better than DSLR's, and are good in low light. These cameras are the logical next step for DSLR or mirrorless shooters who want better image quality and ease of use. These cameras are for serious filmmakers, and should only be bought if you want to, or are going to, be filming a lot.
Consumer Camcorders
Consumer camcorders are the basics for filming. If you're just beginning, or aren't going to be filming much, this is the type of camera you want. Its small and unobtrusive, has good controls, easy to handhold and good image stabilization. They do however, have low image and sound quality compared to a prosumer or pro camera, especially in low light. However, its the perfect choice for beginners, families or school students.
Smartphones and Tablets
These are an unwise choice for a professional filmmaker, but can be useful for researchers and journalists. You can shoot and edit on most smartphones and tablets, and with the right accessories and apps, they can be really useful. They're easy to use and are reasonably small and portable. Unfortunately, sound and image quality won't be as good as a dedicated video camera, and they are awkward to handhold. But these can still be useful to some people, or even for taking pictures of an area you want to film for later viewing.
Compact Still Cameras
Compact Still Cameras can shoot HD video. While this is true, they aren't for filmmaking. These are for traveling and taking pictures. However, if you are short on money, these can be an alternative. Small and unobtrusive, plus a great zoom range, these cameras can be used for filming. However the sound quality won't be great, and you most likely can't connect an external microphone, and they are a bit awkward to use for filmmaking. However, they are always an option.
Action cameras. These little cameras are small and tough. You can mount them onto pretty much anything, which makes them great for aerial shots and first person shots. However, you wouldn't want to use one as your main camera. They have very basic sound, and you're unable to see what you're shooting as it doesn't have a viewfinder. But they can be excellent, if put to the right use.