Tweetcube is a new service built around Twitter API that allows to share files with twitter. Pownce has this feature of sharing files with followers but twitter lacks this one.
Tweetcube is a free service, you can share images, videos, songs, zip files. The upload limit is currently 10MB/file. You can upload unlimited number of files, they will be deleted after 30 days.
Keep in mind that you need to provide twitter username and password to use the service.