HeyPasteIt! is a free web service that allows you to paste the text onto a clipboard on their site where it is then stored at a unique address such as http://www.heypasteit.com/clip/XYZ. You can then access that clip from another computer using that address, copy the text and then paste it to a file or where ever.
I tried it and it worked well. It even handled multi-page clips. However you can't copy and paste images - it's text only. Another reservation is the site doesn't mention how long the clips are kept for. However my test clips were still available a week after creation and that's more than enough for the intended use.
This site is well worth bookmarking. One day you'll need this.
http://www.heypasteit.com