Here is a solution I use with SquashFS. It is quite similar to TAR.GZ solution proposed earlier, but has some major benefits.
SquashFS is a compressed file system, which is completely stored in one file. This file can be mounted to an existing system and accessed in a usual way, like any other partition. The difference to TAR.GZ is that SquashFS is a full-blown file system with random access to files, while TAR is just one big concatenated file.
This means that if you want to mount some large backup of your whole file system, for TAR.GZ it would take like 5 hours (in my experience) and for SquashFS it would take just minutes/seconds. The same is true also for the compression/backup operation, SquashFS is many times faster.
It appears that not only can you mount squashfs file, but also open it as a usual archive with familiar apps like File Roller on Linux and 7-Zip on Windows, etc.
So here is a command I use to back up my root folder:
sudo mksquashfs / /path/to/backup/hdd/root-backup.sqsh -e home media dev run mnt proc sys tmp
where "-e" switch excludes folders you want to exclude (like virtual and external Linux folders in my example).
After the backup is done, I can now mount it:
sudo mkdir /mnt/root_backup
sudo mount /path/to/backup/hdd/root-backup.sqsh /mnt/root_backup -t squashfs -o loop
Now just wait couple minutes (depending on size of the archive) and enjoy all your files at /mnt/root_backup folder.
Same can be done for /home/myname folder, e.g.
sudo mksquashfs /home/myname /path/to/backup/hdd/home-backup.sqsh -e Dropbox GoogleDrive
I exclude Dropbox and GoogleDrive here to avoid any potential problems in the future, in case I restore those folders from backup and they become messing with the actual files in the cloud.
Check more info at http://tldp.org/HOWTO/SquashFS-HOWTO/creatingandusing.html