[I]Do DVD+RW discs need to be finalized?
No. Everytime a DVD+RW disc is ejected, either from a DVD+R/+RW drive in a PC or from a DVD+R/+RW video recorder, it automatically contains the needed information for the disc to be read in a normal DVD-Video player or DVD-ROM drive. There's no need to perform a time-consuming "finalisation" process on the disc, as is required for all other rewritable DVD formats, and for CD-RW. Likewise, there is no such thing as "unfinalizing" a DVD+RW disc: you can always make modifications or add new contents to a disc without performing some special procedure in advance.
Do DVD+R discs need to be finalized?
Yes. In order for a DVD+R disc to be read in a DVD-Video player or on a computer's DVD-ROM drive, it needs to be "finalized". When the disc is finalized, its final Table Of Contents will be written on the location of the disc where a normal DVD player will look for it, and you can no longer add new material to it. Finalization can be done on a DVD+R/+RW video recorder by applying the "Finalization" option on the recorder's on screen menus (see manual). On a PC that uses some form of packet-writing software, you need to select some "close" or "finalize" option from the program's menu to make the disc compatible. When you write a full disc using a DVD authoring package or a copy tool, finalization is usually automatically applied. Note that finalization is not required for reading the disc in a DVD+R/+RW video recorder or a DVD+R/+RW drive. You can add new video segments or data at various time intervals as long as the disc is not finalized. Be aware of the fact that finalization does not exist for DVD+RW: a DVD+RW disc is always immediately DVD compatible. [/I]
From the FAQ at the DVDplusRW.org