For a number of years I've been answering the same question from my wife: "What is the biggest file size that I can attach to an email?" Now the answer to this is straight out of the consultant handbook: "It depends."
It depends on your smtp server's limits, the reciever's limits/security policy/attachment filtering/etc. Even Google Docs has limits for file sizes. There are a number of sites that already provide a service whereby someone can upload a file and get a link to paste into an email, so that the recipient can then download the file later. I even thought of writing one myself. tomczarniecki.com is actually the domain name of my proposed service to do just that. But I got sidetracked by something shiny and the need for the site disappeared as some excellent "competitor" sites appeared.
A couple of weeks ago I was asked the same question again, but it was a bit more important that I gave my wife an answer (or an ability to share very large files). So out came IntelliJ Idea, and after a bit of tinkering the S3DropBox was born. This is a Java Swing application into which you can drag and drop files, which are then uploaded to your Amazon S3 account. You can create public links to these files, and paste these links into emails, so that the files can be downloaded later (using any web browser) by clicking on the link, or you can download the files yourself at a later stage using the S3DropBox.
You can download a platform-independent version, or a Mac OSX .app bundle, or just the source code. As usual, it is a BSD license, so use it however you like, all care and no responsibility :)
A note for beginners with Amazon S3: This service has a concept of buckets that contain objects. With the S3DropBox you can create buckets, and then upload files into these buckets (so that they become objects). If you want to know more about these concepts you can go to the Amazon Web Services page.