I think your tapes will outlast recordable DVDs, but, still having a working player could be a much bigger issue. As I understand it, a modern tape ought to go 50+ years. The biggest problem with *some* tapes is hydrolysis, where the binder (glue-ish stuff) that adheres the iron oxides to the plastic absorbs water. Storing in a low-humidity environment, and even later dehumidifying can even save those.
I've not heard of hydrolysis affecting tapes later than 1985 or so, and low-humidity storage does even the earlier tapes fine.
Really, tapes are a much more permanent medium than recordable DVDs which oxidize, hard drives which bearing lube evaporates, or long-term cloud storage that goes bankrupt, or, service changes / account loss.
As to whether you should just throw them in the trash... it's a hard question to consider if that's going to be where they'll end up anyways in 5 or 10 years.
From the upper left corner of the U.S.
Photos, Video & Pano r us.
College and workshop instructor in video and audio.
70D, Sigma 8mm, Tokina f2.8 11-16, Canon EF-S f2.8 17-55, Sigma f2.8 50-150 EX OS, Tamron 150-600VC. Gigapan Epic Pro, Nodal Ninja 5 & R10.
| 
