What I want exactly is a hard drive to hard drive incremental backup, not an image file. The original HDD has three partitons - ext3, linux-swap, and NTFS. What would be the easiest way to do this free?
Freebyte backup does incremental backups and is free software.
Freebyte Backup is a freeware backup program for Windows. It allows one to easily copy (and filter) a large number of files and directories from various sources into one backup directory. It is possible to backup all files found in the specified set of input directories, or to have only certain file types copied. Files can be filtered according to file-extensions. E.g. you can specify that you want to backup all .doc, .rtf, .jpg, .bmp files, but none of the .exe, .dll and .txt files. You can also very easily define new file extensions inside the filter.
Incremental backup options
With the optional 'Incremental backup' feature, the program only copies files which have not yet been saved by Freebyte Backup. It is also possible to specify a date, so that only files changes/created after a certain date/time are copied, or to only copy files if they are more recent than the corresponding files at the target location.
There is a great article on Backing up Linux and other Unix(-like) systems that is really worth the read.
Maybe Dar is what you're looking for - Full featured archiver with support for differential backups, slices, compression, ATTR/ACL support. DAR also supports Pipes for remote operations, including with ssh.
It looks like you're needing something like Clonezilla (http://clonezilla.org/). It doesn't perform an incremental backup like you had mentioned wanting, but I haven't seen any other imaging software that actually only copies incremental files.
Also, if you were needing an incremental backup solution for the ext3 partition from Windows, you'll of course need to be able to access the partition with something like http://www.fs-driver.org/index.html or http://www.chrysocome.net/explore2fs. After that, you should be able to do incremental backups with SyncBack SE (http://www.2brightsparks.com/freeware/). I'm not sure of a way to access the swap partition though unless explore2fs or the ext2 driver for Windows allows that as well.