DVD-R } Both backed and developed by DVD-RW } Pioneer.

DVD+R } Both backed by Philips, Sony, HP, DVD+RW } Dell, Ricoh, Yamaha

DVD-RAM } A cartridge based Recordable DVD developed by Samsung (I think)

Most DVD-ROM units for computers cannot read any of the recordable DVD formats, but it's and evolving standard. If you wait another month or two you may have more options.

If you want to record DVDs to work with a specific DVD player, I'd check the specs and see if it supports any of the writable formats. I hear that a lot of the Apex home players can play DVD-R and DVD-RW. And the Samsung DVD V1000 reads everything but DVD+RW and RAM.