You must know wetransfer, which provides easy and fast server based large file sending. It's great for files smaller than 2GB if you don't mind the ads you have to look at while uploading and downloading. With wetransfer you must first upload your file to an amazon cloud server, then your recipient gets a link for the file download. The advantage is that the download is really fast and the service is free. For a fee you can get your own channel so your recipient can look at your ads instead third party ads.
There is also a new player in town when it comes to large file sending. Sendoid uses P2P technology, which means your and your recipient's computers are connected directly without a server in between. Once you select the file to be sent you get a download link instantly which you can share with your friend or colleague and they can start downloading instantly. Optionally you can also set a password for added security. Here the download speed is limited by your upload speed, so it's a bit like sending files through Skype or other chat service, however there is no size limit if you use the Sendoid desktop AIR application. Sendoid is also free and there is no pay option at present.