(unprivileged commands follow)
dd if=/dev/zero of=~/zeros bs=1M; sync; rm ~/zeros
Compressing on the fly can be slower than your network bandwidth depending on your network speed, your processor(s) speed, and the compression level, so you typically tune the compression level (because the other two variables are not so easy to change). Example backup:
(privileged commands follow)
pv < /dev/sda | pigz -9 | ssh user@remote.system dd of=compressed.sda.gz bs=1M
(Note that on slower systems the ssh encryption can also slow things down.)
Some sharp people may notice that it's not necessarily a good idea to back up a live system this way because the filesystem is changing while the system runs. It's usually just fine on an unloaded system that uses a journaling filesystem.