DVD-RAM is mega lame
it is completely incompatible with other DVD players, DVD-ROMs, etc.
DVD-R is write-once, usually 4.7GB, compatible with most players (home systems and DVD-ROMs), there are 2 types, DVD-R Authoring and DVD-R General. The general version is more common.
DVD-RW is re-writable (approx 1000 times), 4.7GB, based on DVD-R. This is the re-writable format the Pioneer DVR-A03 and Panasonic LF-D311 use.
DVD+RW is re-writable (approx 1000 times), 4.7GB, slightly more compatible than DVD-RW with existing equipment. Discs can be written using CLV and CAV (other formats can only use CLV), which means it is better for storing data (CAV means faster access times). DVD+RW can currently be recorded at 2.5x speed, while DVD-RW is currently limited to 1x. Also, DVD+RW includes built-in Mt. Rainier support (DVD+MRW) which gives improved packet writing support. (The HP DVD100i, Philips DVDRW208, and Ricoh MP5120A use this format.)
DVD+R will be out early next year. It is write-once, 4.7GB, based on DVD+RW.
In short, it appears DVD+RW is the best re-writable format, but that doesn't guarantee it will win out. (See VHS vs. BETAMAX)