On the Script-Tutorials.com site there's a new tutorial showing how to use the Vimeo API to upload your content to their service:

Today I would like to continue talking about video. Last time we talked about Youtube, but today I decided to select Vimeo. [...] Our second example – Vimeo. In our new tutorial I will tell you how you can create Vimeo cross-uploader for your website. To achieve our idea we will use Vimeo Upload API. In the beginning, we should register at Vimeo here.

The full code for the upload script, the HTML for the frontend for it and the CSS to give it a little bit of style. You can see a demo of it here or just download the source.