Is it possible to limit the number of versions stashed by Amazon S3's versioning?

While I don't believe Amazon added the option to limit the versions to a specific count of revisions (say "5" previous revisions), you can certainly use S3 lifecycle management, which does support rules based on time. You can use NoncurrentVersionTransition to transition the old version to a different storage class, and you can use NoncurrentVersionExpiration to finally delete an old revision.

So if you backup your data at a predefined time interval (say once a week), then if you set your NoncurrentVersionExpiration to 6 weeks, you'll only keep the last 5 (maybe 6?) versions.

Reference: AWS S3 Lifecycle

Currently you would need to list and erase old versions manually, as there is no user defined version limit.