Unfortunately, I haven't had luck with Open Source backup software that uses it (the shadow copy snapshot would fail, the error code would be no help, and finding no resources, I gave up), but commercial software I've used was great. When I was at a big corp, the commercial backup software whose name escapes me at the moment would litterally wait for files to be saved, then do an incremental backup.
As of now, I'm using Veeam on my personal machines, and it runs an incremental backup nightly and saves to an smb share.
I've been using urbackup for years. It does disk image-based backups and/or file-based backups. Disk image-based backups are incremental at the block level, and file-based backups are incremental at the file level (so if a single byte of the file has changed, the entire file gets backed up). It uses the Volume Shadow Copy mechanism that the sibling comment mentioned to get atomicity and avoid file locking issues.
