I remember all the disconnects with ICQ file transfers. I think they added a recovery mechanism eventually.
Some friends even ran their own ftp (I think most people used War ftp) before ISPs started blocking ports.
Now it's all about uploading to "the cloud" or use sneakernet. My friend uses mega.nz, which seems decent for file sharing. I, personally, never underestimate the bandwidth of a sedan, driving down the highway with a single USB key.