I just installed Multibit HD, did a few transactions, and I already have 15 .zip.aes backup files? Do I have to keep all of these forever, or only the most recent one?
I think you want to take a look at the Backups help page on multibit.org.
I can't say for certain (as the wording is a tiny bit vague here), but I am pretty sure that each of these are what they're referring to as "rolling backups" which "encrypt a snapshot of the current wallet".
If that's true, then each one of these contains the previous ones, so you would only need to keep the most recent one.
Either way, if MultiBit is doing it's job right (and I suspect it is), your seed phrase (what MB calls "wallet words") should be enough to recover your wallet no matter what. To quote them, "You can always recover your bitcoin through your wallet words (seed phrase)."