Maybe I'm living in cloud cuckoo land.
I'd like to be able to offer some video and audio material via my own website and use something like Paypal to charge people to watch the video and to download the audio. Relatively small amounts of money.
Does anyone know if this is possible?

It is certainly possible. Here is one solution:

MOD Machine at Leaping Brain Labs, Inc. (http://leapingbrain.com/mod-machine)

It is certainly possible. Here is one solution:
MOD Machine at Leaping Brain Labs, Inc. (http://leapingbrain.com/mod-machine)
This business model wouldn't work for me.
Does anyone know of any way that you can simply and cheaply organise for someone to pay before streaming or downloading eg using Paypal?

The most basic way would be to use the built in password/user system of a web server. When someone buys a viewing package from you, you activate an account for them so they can access a page that is protected. This requires that you have access to such features. Some webhosts like 1and1 let you create protected direcories but if you have your own dedicated server, you would be set. After that places that allow protection of digital downloads such as the one above or E-junkie Shopping Cart for selling downloads & tangible goods (http://www.e-junkie.com)

Thank you Josh
This is really helpful.

Maybe something like this?
HD Stock Footage - High Definition Video Stock Footage - Royalty Free Stock Footage (http://www.alwayshd.com/home.php)

Thanks Noah. This is heading in the right direction but if I am reading it correctly I would have to upload material to the Always HD website and viewers would have to look for it there. What I'm hoping to do is to embed video into a website that I control and charge for access to it.