YouTube has lost 20 Million dollars to date and they haven't even factored in their upcoming legal costs
YouTube is worth a lot to google however because they have advertising to push out. Rather than do what they did with MySpace (Pay for advertising space)...they spent a few more bucks and bought the whole shebang with YouTube.
YouTube's long term profitability though fully depends on 2 things:
1) If it survives the legal battle that is to come
2) If people still are interested in it when its all college kids uploading camera phone videos and not every obscure video that's ever been on TV. YouTube is already developing a technology to automatically sniff out copyrighted material from an exisiting database of media. The question in my mind is not...will youtube be able to make themselves legal. But instead it is...will YouTube be anywhere near as popular once it IS legal. If they can survive #1 then it will continue to grow in popularity. If they lose #2 then in my opinion is a HUGE liability asset for google.