Would any of you store a video file as a binary object in a RDBMS such SQL Server?

You should take care when storing blobs in a db.

Most importantly, WHY do you want to do it?

Well we have a product catalogue of video training material, and each item described in the database has a video or audio item associated with it. We also have three branches in South Africa and it would be ideal if the data could be replicated to all three branches. Would it be better to use a file system and just keep a record of the path in the database instead?

Depends on your requirements though (people have been known to f^%$ around file shares where they are not supposed to be).

If you do go for it, just make sure you have proper maintenance plans in place (your log files will go ape quickly), and also store the blobs in a separate table than the actual file information (with just a link the the info).