There are a number of hosting companies with ffmpeg support, this post is a comparison between them.
pacifichost.com They promise unlimited web space and bandwidth, but if your site uses more then 100 giga of bandwidth in a month they will quickly suspend your account for over use of server resources. The smallest plan they have is $2.49 a month, but they will ask you to pay for one year. Pacific Host, is relatively a new company and most customers reviews are quite bad.
www.cheapwebhostinghouse.com The first hosting company which started to offer ffmpeg on their shared hosting plans. Really a basic site, with a free billing system. The company belongs to Hosting Marketers, which is on video streaming since 2005. Cheaphosting house, the basic hosting plan comes with 2000 mega (2giga) of web space and 85 giga of bandwidth, it is small but you pay monthly, and the cost is $2.95 a month, paid monthly. The bigger plan they have is 20 giga of web space and 1500 giga of bandwidth at the really nice price of $14.95.
cirtexhosting.com they promise unlimited everything, but as soon as you really have a productive site they will contact you to upgrade because you using too much server resources. The prices start at $2.49 and to have this price you need to pay for two years, if not the price is $5.99 and you have to pay 6 months.