No one can know the future, so we can't say anything for sure. But for now, having the 24 words seed is everything you need to recover your wallet with or without a new device.
I'm asking because I just bought a Ledger Nano S, and I want to store a few coins in there and then wander off to Nepal/Tibet/India and become an itinerant monk. But in case I ever want to come back (let's say 20 or 40 years in the future), I want to be able to retrieve my old coins, which might be worth a lot by then.
Wow! That's actually pretty cool.
But could I also recover the wallet if there were no more ledger devices on the planet? (Highly unlikely, but I still want to know)
Yes. You can import your Ledger wallet into any software that has support for BIP 39/BIP 44 seeds. So having a Ledger device isn't necessary.
Or would it be better/safer to find out what the private key of the wallet is (I read there are applications that tell you the private key when you provide the 24 words and the passphrase) and store that on paper and different USB-Sticks (and give that to friends/family)? Or would that be unnecessary?
For now, this isn't necessary. But as I said, no one predict say what will happen in 20-30 years, right?
If in the future, there is still a way to get your private-keys derived from the seed, you won't need to do that. But if for any reason (I can't think of any), that's not possible anymore, then having the private-keys will save you.
In the end, it's up to you to decide if you want to manually get your private-keys and save them in a different paper/flash drive.