While Spideroak is my go-to for deeper and more long term offsite backup, for quickly moving things between computers, or to my phone or tablet, I have been looking for a replacement for Dropbox since the revelations that their cloud service is not exactly the most secure out there. I think I have found a good solution in Ubuntu One, which is built into the Ubuntu OS.
Ubuntu One runs very similarly to Dropbox. You can choose what folders you want synced and they will be viewable on all devices you have the app installed. I find Ubuntu One to be very fast and works smoothly on both the desktop and phone. My primary uses for Ubuntu One are twofold. First to move files to my phone, since the Galaxy S3 that does not allow access on Linux computers for some reason (oh, I know: Google wants you to use their Music Cloud service. No thanks). Second, I use it for moving files from my day to day use laptop over to my desktop where I can print things or to my work computer, which I do not do that often.
Ubuntu One is a sold Dropbox replacemant. I can see myself getting a lot of use out of it in the future.