DVD-RW: DVD-R is short for DVD-recordable. (Note the dash before the R; it's pretty important.) Like your old friend the CD-R disc, a DVD-R disc can be recorded only once. However, the DVD-R can hold a whopping 4.7GB per side of the disc, for a total of 9.4GB of data on a double-sided disc. DVD-R is the darling of the video-editing crowd, because it allows you to record a disc that you can use in a standard DVD player. Naturally, the DVDs that you create with a DVD-R drive can't be read on a standard CD-ROM drive (but you can burn regular CD-R and CD-RW discs).
On the rewritable side, the DVD-R disc format is called DVD-RW. These discs can also store 4.7GB, and you format them much like you format a CD-RW disc. Any DVD-ROM drive should be able to read a DVD-RW disc. Unfortunately, not all DVD players can read DVD-RWs, so if you're an up-and-coming Hollywood type that's interested in producing your own movie discs, you should stick with the DVD-R standard (which is compatible with all DVD players).
Pick DVD-R/W if you're looking for the highest level of compatibility with all DVD-ROM drives or you're distributing discs to others.
DVD+R/W: The other independent DVD standard, DVD+R/W, is widely available as well. This more recent format is being touted by an entirely different group of computer hardware manufacturers. DVD+R discs and DVD+RW discs can store 4.7GB, and a DVD-ROM player can read both types of discs. Again, however, you run into the same problem - DVD+R discs are compatible with most DVD players, but DVD+RW discs aren't widely supported by DVD players. Plus, DVD-R/W and DVD+R/W are incompatible.
Pick DVD+R/W if you're looking for compatibility with the latest DVD-ROM drives or you want to spend a little less on media.
DVD-RAM: Finally, you have good old DVD-RAM - a rewritable disc that can store as much as 9.4GB of data by using both sides. (A double-sided DVD doesn't have a standard label; printing can appear only around the spindle hole.)
DVD-RAM is well established, and no "plus" format is competing for fame and fortune. DVD-RAM is a great option for storing those huge digital video files, and because DVD-RAM discs are reusable, they're the best media for backing up hard drives. Note, however, that most DVD-ROM players can't read DVD-RAM discs, so use one of the other DVD formats if you're recording something to distribute to others.
Choose DVD-RAM if compatibility with DVD-ROM drives is not an issue, such as when you're creating backups or discs that you read only on your computer, and you want to rewrite the largest amount of data on an existing disc.