There are two new plugins you should be excited about if you wish to put WordPress media on Amazon's S3 service.
WP Offload S3 has been around for a few years, but has been completely rewritten over the last several months, to go along with a name change. WP Offload S3 is by Delicious Brains, the makers of WP Migrate DB Pro, and Brad has been chronicling some of the development progress on ApplyFilters.
The pro version of WP Offload S3 is coming really soon, and will enable additional features, like migrating old media files to S3 for you, WooCommerce and EDD support, and handling changes to media URLs in your content if you change your AWS settings. You can see some of the features and notes in their already published docs.
WP Offload S3 also offers support for Amazon's CloudFront CDN service. WP Offload S3 looks like it will be a nice freemium product for Delicious Brains, and they've invested a lot of man hours making sure it works well.
The second plugin, which is a bit more developer focused, was released by Human Made today. Available on Github now, they've released S3 Uploads, which is a drop-in plugin to completely replace the WordPress upload system.
S3 Uploads looks really nice, and the configuration is completely in code, so it's probably not the best option for non-developers.
One cool thing about S3 Uploads is that it bypasses WordPress entirely, so that migrations of sites with big media libraries are much easier. WP Offload S3 doesn't offer this option, but instead uploads to your media folder, copies to S3, then gives the option to delete from your media folder. Depending on the use case, one or the other may be preferable for your site.
It's nice to have two solid options for S3 all of a sudden. I love Amazon S3 and it's super affordable. Now just to choose which one is right in any particular scenario.