My Magnavox DVD recorder died on me before I could finalize the DVD's that I already had copied clips from my video camera onto. I can't watch them now and have no idea how to finalize them. Any suggestions?

You would have to get another of the same machine to finalize them on. You can find them on eBay. I bought one of those Magnavox's for about $125 there last year.

would I need to get exactly the same product I was using? It's really old.

If it's from 2009 or so, it's made by Funai which is the same as Philips or SV2000 (or something like that, it was a $49 model at Walmart.) Discs burned on those are cross-compatible. This is why I only burn onto +RWs though, you can play those on any machine right away then copy anything you want to keep onto a non-rewritable disc.

Is this Magnavox you were using? This is the one I use. I found a brand new one on eBay last year for $125. Most of them are refurbished or used since they no longer make them anymore.