I've said this before, but I'll say it again because it's always useful in these threads...

I believe that a well designed paper ballot system is superior to any paper-free system. Furthermore, I think the concerns of the general public about what is actually problematic in elections (and what solutions can work) are generally wrong. I'm basing this on my experience as an election judge in Minnesota. I'll describe the system, and you can decide for yourself.

Minnesota uses paper ballots read by Scantron machines - the sort of bubble-marked sheets you used for tests as a kid. We have same-day registration and provisional ballots available for unregistered or incorrectly registered voters. We do not require ID for ordinary registered voters. There have been two statewide recounts in recent years - the 2010 governor's race, and the national-profile 2008 Franken/Coleman Senate race recount.

Now, the process. First and foremost, all activities that require handling ballots, whether marked or unmarked, sealed or open, must be done in the presence of representatives of at least two political parties. It is flatly illegal for one party to handle ballots alone. This prevents all sorts of fraud - either adding fraudulent ballots, or removing marked ballots.

Second, a simple paper tally is kept of the number of ballots cast in each precinct. At count time, the number of votes counted by the machines must exactly match the number of ballots given to voters. A mismatch triggers a hand recount of the precinct and a bunch of other validation bureaucracy. This checksum also prevents the addition/subtraction of ballots at the precinct level.

Voter machine tallies are spot-checked by hand counts of individual machines - not enough to slow down the process, but enough to insure that there was no large-scale alteration of machine behavior.

Registered voters are on paper rolls. When a registered voter arrives, their name is marked off the list and they are given their ballot. If someone tries to vote twice as the same person, it's caught (and triggers bureaucracy). Their ID is not checked. Same-day registration requires ID and proof of precinct residency; the valid documents are well specified (utility bills, etc).

Political parties are invited to have poll monitors at any and all precincts, to keep an eye on the process. The poll watchers do not touch ballots or participate in the count, but are welcome to observe. They can also challenge individual voters, which makes ballots provisional and may lead to ID requirements. (I remember in 2004, the Democratic poll monitor was convinced the Republican monitor would challenge every single brown-skinned person in the precinct, and the Republican was convinced the Democrats would bring busloads of fake voters in from Wisconsin or something. Needless to say, both were wrong.)

The result of all of this is that highly accurate informal counts are available on election night, thanks to machine voting, but manual recounts are always available, thanks to the paper. And the integrity of paper ballots is strongly protected by process.

The only even arguable gap is the idea of fraudulent voting by using other people's registrations, or fake registrations. But actually doing this at a scale large enough to matter is difficult and risky. Minnesota presidential elections draw about 1.5M voters. To alter the results by 1% would require 15,000 fraudulent votes. If someone could vote once an hour, they could maybe vote 15 times. You'd need a thousand people, with training, transportation, and written data. It's hard to keep conspiracy at that scale secret.

So yeah. This is trustworthy. And it's simple. It doesn't require exotic technology. It's mostly just good bureaucracy.