Ask, and you shall receive.
We’ve just unrolled a new feature on the site, Downloads. This lets you upload any file you want to your repository, be it public or private. The files are uploaded directly to Amazon S3, so our servers won’t even break a sweat.
After the upload is complete, your file will be accessible via the Cloudfront content delivery network (CDN), which allows for extremely fast downloads, all over the globe. If a repository is private, the URL for downloading a file will look a bit different (it will include an authentication token that is good for 24 hours), but that also means that your files are not accessible to anyone else, even if they have the full URL. For public files, they will be served from cdn.bitbucket.org/username/reponame/downloads/.
Files uploaded will count against your quota, but Mercurial repositories being notoriously small, you should have plenty of space, even on the free plan.
Some of our users have already begun upload, as can be seen here and here.
On another note, tags are now ordered by date instead of alphabetically.
A big thanks to Vetle Roeim for spending some time helping us out with this feature.