Here in San Mateo County, we have a good voting machine system, although the knob-based UI is strange. After you've selected all your votes, you press the "done" button, and, behind a transparent window, a printer prints your votes on paper, with the chosen candidates names spelled out fully, followed by a big 2D bar code. You can then accept or cancel your vote. If you reject the printed version, it prints CANCELED and you start over. If you accept, it prints VOTED, and the paper roll winds past the window.
The paper is a backup. The votes are also recorded by the software. But the paper can be read by hand if necessary, or by a scanner which reads the bar codes. So recounts are possible and checkable by all parties.
It's possible to make verifiable secret systems.
Some have even been tested in real elections in the US as part o projects by NIST (for arcane reasons, NIST controls voting technology in the US :P).
For example, Takoma park in maryland has used scantegrity a few times (2009, 2011).
The paper is a backup. The votes are also recorded by the software. But the paper can be read by hand if necessary, or by a scanner which reads the bar codes. So recounts are possible and checkable by all parties.