It would help to know which burner you have and the type of dvds you are using.
We recommend Verbatim as a safe choice of media for most dvd burners. You can find Verbatim at local shops like Best Buy.
If you'd like to order online, you might want to try Taiyo Yuden 8x +R disks. They tend to be very reliable and compatible. You can find them at shops like rima.com and supermediastore.com, among others. This assumes you are in the US. If you are located elsewhere, we may be able to point out other shops to buy from.
We also recommend not burning at maximum speed. If you have 16x disks, try burning at 8x.
Perhaps you'd like to outline your backup process for us...tell us the programs you are using.