DVD-R/RW
The originating DVD format that was compatible with most DVD players is DVD-R/RW. DVD-R/RW supports both single-sided (4.7 GB) and double-sided (9.4 GB) media. Due to the amount of time that DVD-R/RW has been out, many more stand alone DVD player are likely to support them. This format is pretty much your everyday use format. It is advised to use this format if you intend to create home movies, and other applications that would run from a stand-alone DVD player.
DVD+R/RW
The new format is DVD+R/RW, which happens to be based on CD-RW technology. This format is becoming increasingly popular. The compatibility rate of this format however is not as high as the older format on stand-alone players. The introduction of the DVD+R/RW was created in the intent that the format would be completely compatible across both DVD optical drives in computers, and drives in stand-alone players. The format also allows for a mix of information on the media, such as not only video, but also data files. This is not to say that the previous format cannot be used for data, it is just to say that the creators of this format felt DVD+R/RW was a much better format to be used for both purposes. The DVD+R/RW format supports both CAV and CLV writing as well as lossless linking. CAV is an acronym for Constant Angular Velocity. This feature pretty much means that the data transfers at the same speed regardless of where it is being read off the disc; as opposed to Constant Linear Velocity which is dependant on the location of the disc being read. CLV is the method of transfer used by most of the older optical drives. The introduction of CAV allows the drive unit to operate without much trouble as it does not have to regulate the motor speed. This is an improvement over CLV which can run into problems on higher speed optical devices because of the brief latency when changing motor speed. Currently most DVD+R media are capable of writing at a maximum of 8x where as DVD-R is still at a 4x specification.