I've been keeping an eye out for a simple way to share a large file (1-5 GB) to another person over the internet privately, and I finally found something that I like. Sendoid.
The uploader and downloader can use it either from the web page or from the client app they provide. However, if you use the client app you get the ability to resume a transfer in the event that it's interrupted, which is very important for large files.
You can have multiple people downloading from you at the same time, and when you're done, remove the file from the list or close the app. Very simple, no registration or signup required.