I'm looking for a peice of software I can download that will allow me to
upload short videos to my own site and then show them in a custom
player.

I know for example youtube / video egg allow you to upload videos to
their site and include a snippet of code to display it on my own site.

What i'd like to do is have that all hosted on my own site. Anyone know
of any software out there that do this. I thought video egg did but it
seems you need to be a partner with 1,000,000 unique visitors a month to
be eligible for theirs.

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JShopDesigns.co.uk - Custom E-Commerce Design and Development.
Personal Blog - Project & Employee time tracking software

If you have flash you can use the built in video player.
This is a popular choice too > JW FLV Player