This sounds like a problem only techies have, and already have solutions for, like centralized file servers. I don't sync files, I keep one copy of my files, and access them over the network.
I have a large music/photo collection I sync with AeroFS.
I have multiple machines on my network with ten's of GB of spare disk space, so this provides a good backup policy without needing to consider how I should back up all that data off a central file server.
I am probably the perfect target customer for this: I love and depend on Dropbox for a lot of things since I'm on the move all the time, but I do not trust them with my sensitive data (and I include in this category all of my business data - invoices, et. al). I already have a cheap, mass-storage server colo'd for offsite backups, so being able to run my own copy on my own hardware is a godsend for me.
I would say AeroFS is as easy as it gets when it comes to transferring large-size files between computers on the Internet. I use AeroFS to share photos and videos with my parents across the Pacific. Works pretty well.
I have multiple machines on my network with ten's of GB of spare disk space, so this provides a good backup policy without needing to consider how I should back up all that data off a central file server.