The divide between Web IM apps and the software versions is getting smaller, albeit with the help of improved bandwidth and technology like Adobe's Flash. In the same vein, Meebo, the popular Web-based multiclient chat platform is getting a handy update tonight. Users are now able to trade files with each other right in the chat window. It's not just Meebo users, either, it's anyone on your friends list. If your buddy has a file-transfer-enabled client, you'll be able to pass files back and forth freely.
However, unlike software IM clients, the caps for file transfer are very stringent at 10MB per file, and 30MB of total transfers per month, meaning you're not going to be able to pass around video clips or other large files, especially to more than one or two buddies, before hitting your limit.
The Meebo team has employed a combination of Amazon's Web Services to make the transferring possible, including EC2 for scaling and S3 for storage. Safari and Opera users are out of luck, however; the Meebo team has only got it working for Internet Explorer and Firefox. Safari support is on the way "soon." In the meantime, the upgrade is good for casual and occasional file swapping, but with these limits you're better off sticking to e-mail attachments or a quick-and-dirty file-drop-and-share service like Divshare.