So Dropbox ended support for PowerPC. That happened. Going forward, their client will require Snow Leopard, and not only that, but the old clients will stop functioning so you'll only be able to access your data through their web interface. The official cutoff date is May 18, but to try mitigate this and at least get Dropbox to allow PowerPC users to continue using their old clients, Martin Kukač from viva PowerPC has posted an open letter urging just that. You can read the whole thing here:
Also, to add your voice and show Dropbox there's still a demand from PowerPC users, you can go to their forums and post to this somewhat long thread, or even start your own.
As for Dropbox alternatives, I hear second-hand that SugarSync still works with their old Tiger client (direct download). Also, you can try Unison, which I wrote about awhile back. If you're syncing several PCs/devices with Dropbox and only one PowerPC Mac, perhaps you can sync your Dropbox folder with Unison. It's not totally seamless, but it may be workable. If you want to share files with a group of collaborators, you can look into Box.com. They support WebDAV as does Cyberduck, so uploading or downloading the latest file versions with Cyberduck as your client is simple and quick. And if you're accustomed to using Dropbox to transfer individual files to and from your iOS devices, DropCopy can do that for you, too (Tiger and Leopard users, download the Older Version).
As for me, I don't sync on the cloud. I use Unison to sync over my home network. I have to take my Luddite nomenclature seriously.
UPDATE: The editors at LowEndMac have put up a petition at Change.org: Continue to support Dropbox on Mac OS X 10.4 and 10.5.