The buzz I'm getting about the two (currently) competing DVD formats is:
DVD+R is actually meant for "real-time" recording. Say you have a video surveillance system, using digital cameras. Chances are the digital video deck uses DVD+R format discs to record the action.
Also, if you are doing computer back-ups to a digital format, then DVD+R allows (so I have heard) better real-time recording.
At this time, there are multi-format, external drives that record using either DVD+R or DVD-R media. A relatively new player in the mix are the dual-layer or double-layer drives, which seem to be more compatible with either media. (Read the specs on the box before making a purchase!) The big thing is that DVD-R seems to be more compatible with table-top DVD players, so if you are burning a disc to view on your home video system, DVD-R might be a better choice. (Again, check your player's specifications.)
The latest member in the alphabet soup of DVD terms is "Blu-Ray." Blu-Ray players are currently quite pricey (about $1,000) and there is a question of their backward compatibility with other existing formats. I have also heard of DVD-R+, which offers over 9 hours recording capability. The best thing to do is search on Google, using "DVD formats" as your search query. Don't be surprised to find a lot of contradicting and confusing information! At the present time, there is no standard format.