Hmm, interesting. In Australia (or Queensland at least) for the local, state, and federal elections, I didn't need to show anything. For the federal election a couple of years back, I just gave them my name, they crossed me off, and gave me some ballot sheets. For the local and state elections this year, I received two letters from the Queensland Electoral Commission, with a little portion to cut out with my details on. I just gave it to the volunteers at the polling place in my electorate, was crossed off, and given ballot sheets.
I suppose there's no need for ID. If you don't vote, you'll get fined. If you vote a second time, they'll know, so you'll either fail in fraud, or commit fraud and cop a fine (and later get hit hard for fraud). Plus, who the hell wants to go back a second time and be harangued by people handing out pamphlets?
It's because in Germany there's a mandetory ID card issued to all civilians, while in America there isn't and the ID's asked for to vote are all optional ones.
Therefore, for an American to vote, they'd have to be forced to go through all the hassle of getting a valid ID simply to engage in their right to vote, rather than letting them have the choice of living without a passport/drivers liscense and still engage in voting.
Most places do not require ID to vote, and it's a controversial issue. People don't want to have to show an ID they are not legally obligated to possess in to exercise a fundamental constitutional right.
It's becoming law in some states, but its far from universal. In some places which have passed voter ID laws recently, enforcement of them for this election has been blocked by courts, since there would not necessarily have been enough time for those who lack ID to obtain it.
Since government-issued IDs also usually cost money, there's a real question as to whether a requirement for ID amounts to a polling tax, and such taxes are generally illegal, not least because they've been used in the past to unequally deny the vote to poorer minorities.
Yes, it's common practice in the US. There is a debate about the law needing to be changed currently going on. The people for it argue, like you said, that voter fraud is very easy. The people against it argue that it would discourage people from voting since ID costs money and time and such.
So yes it's an issue, as to the solution; that's gonna have to be discussed.