There are several other excellent answers here, but let me try to boil it down:
1. Voting is a constitutional right.
This is the central point, and one I didn't see mentioned in other answers. You can't compare it to needing ID to drive or board a plane, since those aren't guaranteed in the constitution:
15th Amendment (1870): The right of citizens of the United States to vote shall not be denied or abridged by the United States or by any State on account of race, color, or previous condition of servitude.
19th Amendment (1920): The right of citizens of the United States to vote shall not be denied or abridged by the United States or by any State on account of sex.
24th Amendment (1964): The right of citizens of the United States to vote in any primary or other election for President or Vice President, for electors for President or Vice President, or for Senator or Representative in Congress, shall not be denied or abridged by the United States or any State by reason of failure to pay any poll tax or other tax.
26th Amendment (1971): The right of citizens of the United States, who are eighteen years of age or older, to vote shall not be denied or abridged by the United States or by any State on account of age.
The 1965 Voting Rights Act adds additional specific provisions about what states can and cannot do with local voting laws and practice.
US courts have allowed some Voter ID laws, and struck down others as a violation of the constitution or of the voting rights act:
Lots of further detail that I won't get into here, including the distinction between "disparate impact" vs "disparate treatment" and the 2013 Supreme Court ruling that invalidated portions of the Voting Rights Act which led to a wave of new Voter ID laws, but understanding the importance of this issue from a constitutional basis is an important place to start.
2. Millions of US citizens don't have a government-issued ID.
Some estimates suggest that over three millions Americans don't have a government-issued photo ID:
The most common form of government-issued ID are driver's licenses and so the people who are most unlikely to drive, as it is, is elderly, the poor, people who live in big cities, like African-Americans, especially young people, too, especially if they attend college. They may not have need for a car at the moment.
And then people who are in rural areas. The other challenge for them is they are not near the Department of Motor Vehicles offices, etc., etc. where you would get these IDs.
Well, can't all these people just go get some ID? Some can, others cannot (from the same article above):
Many of them never had birth certificates to begin with, and if they did, they were incorrectly - their names were incorrectly put onto these documents. And if that's the case, then you're not going to get an ID. They will not accept discrepancies between your birth certificate and other forms of ID that you may have, like a Social Security card and those kinds of things.
Lots of other stories that emphasize the fact that getting ID is much more difficult if you are elderly, or poor, minority, or don't have reliable transportation.
Some state's laws do attempt to provide better methods for people who don't have them to get IDs, or provide ways for voters to cast "provisional" ballots if they can't obtain ID.
3. The US has a long ugly history of disenfranchisement and voter suppression
Read up on Jim Crow laws, including poll taxes, literacy tests and grandfather clauses.
Opponents argue that Voter ID laws (and other practices like voter roll purges, polling place indequalities, and DMV office closures) are a modern form of voter suppression.
So, is that a plausible argument? How would Voter ID laws disenfranchise certain groups of voters?
If the percentage of citizens without ID were evenly distributed throughout the population (when measured by party, by race, by age, by gender, or by income), then no, Voter ID laws would impact all those groups the same.
But is that the case? No.
So no, different groups are not equally impacted by Voter ID laws. Those in lower income brackets, minorities, and college students are three demographics that are disproportionately impacted, they also tend to vote disproportionately Democratic.
Is it coincidence, then, that more Republicans than Democrats tend to support restrictive Voter ID laws?
The statistics by themselves are no smoking gun, of course. But some Republicans have been a little less circumspect about deliberately attempting to tip the scales:
Representative Glenn Grothman, Republican of Wisconsin, predicted in a television interview that the state’s photo ID law would weaken the Democratic presidential candidate Hillary Clinton’s chances of winning the state in November’s election...
In Florida, both the state’s former Republican Party chairman, Jim Greer, and its former Republican governor, Charlie Crist, told The Palm Beach Post in 2012 that the state’s voter ID law was devised to suppress Democratic votes.
From the same article, a staffer relays what happened during a Wisconsin Republican caucus meeting:
"I was in the closed Senate Republican Caucus when the final round of multiple Voter ID bills were being discussed. A handful of the GOP Senators were giddy about the ramifications and literally singled out the prospects of suppressing minority and college voters. Think about that for a minute. Elected officials planning and happy to help deny a fellow American’s constitutional right to vote in order to increase their own chances to hang onto power."
4. Are more restrictive Voter ID laws necessary to ensure the integrity of elections?
To be clear, this isn't just about whether some form of identification should be required to vote, this is about efforts to narrow the types of IDs that are acceptable. This page has a good timeline of voter ID laws in the US, this chart is a nice summary:
I'm not going to through the differences between all these categories (they vary widely by state anyway), but it is worth discussing the two least restrictive ones:
- No ID Required: The voter is still typically required to find their name in the pre-printed registry and sign, under penalty of perjury, that they are who they say they are.
- Non-strict, non-photo: If the voter doesn't have picture ID, they can show a utility bill with their name and address, or perhaps a voting reminder card send from the state.
It is worth stopping here and asking the question: are these measures sufficient? Have there been vast number of people swearing, under penalty of perjury, that they are someone else? Do people routinely print fake utility bills on their home computer just so they can go vote more than once?
Overwhelmingly, the research says no, in-person voter impersonation is almost non-existent. This 2012 report found a whopping 10 cases of in-person voter impersonation since 2000.
But that's 10 more cases than there should be, right???
Perhaps, but should we disenfranchise millions of voters all to prevent these 10 cases?
That's why Voter ID laws are controversial.