Honestly, I thought this was a stupid question until I interacted with another user on a particular question. The question is, should users vote on answers? If so, why? This other user claims to have a policy for himself to never vote, arguing that leaving a quality comment is sufficient. Is this the case?
Voting is probably the third most important aspect of the site. (Right behind asking and answering)
Voting is important because it shows that other people have 'vetted' the answer. Anyone can post an answer on the site, so how do we know if it is any good? By the votes it gets.
Voting changes the order that answers appear below a question. It helps the best answer bubble up to the top of a list of mediocre answers. This way, when someone finds the question through Google, they can immediately see which answer was the best. This helps separate Stack Overflow from the general forum.
If no one votes how are other users going to know what are the good answers and perhaps more importantly what are the bad answers?
As @jjnguy points out it shows that at least one other set of eyes has seen and reviewed the answer. It's a form of peer review as well as being a rating system. The default view is for answers to be sorted by votes so the most highly voted answer (and therefore hopefully the most correct one) is right there under the question for others to find easily.
People won't read all of the comments so won't see a "this is a good answer" comment.
The vote up privilege page explains it pretty well, and there's a blog entry about voting in general that applies to answers. Besides rewarding people who post good answers (which encourages them to post more good answers), probably the most important reason is to sort the answers by quality. Answers are defaultly sorted by votes:
By upvoting the best answers, you're ensuring people see the most helpful information immediately; similarly by downvoting wrong answers you indicate that they're wrong and push them below more helpful posts
I find myself agreeing with this somewhat:
I don't think it's most voters who don't know the right answer, but this is the reason why I personally don't use all my votes every day. I just don't know enough to cast an informed vote on that many things.
However, if I know enough to leave a comment, then I've probably done enough testing and checking to cast a vote.
I've decided to answer, despite being absolutely unwilling to go into a political (which voting is) argument.
For starters, I am the original user who doesn't vote. Why? I see no reason to.
Most importantly: votes are anonymous. So there is exactly zero motivation on my part to cheer up based on whether the crowd likes or not. I don't care about whether the answer is popular or not; I care about whether it's correct or not. If it's not correct, someone will remark on what is wrong with it.
A signed message praising the answer could be a bonus, but it ends there. Constructive criticism is just as welcome.
Now back to the anonymity part: I dare say, nowadays, most developers and people coming to this site are mediocre (at best) developers. I have no experience with the sister sites. Not all, but most. I don't wish to insult anyone personally. It's just what happened to the software business in the last two decades. The sheer amount of downright not-smart questions is evidence.
There is some truth in selecting a good answer if you have fallen upon the question via some search and it's not your own. A highly scored answer could be good, yet I see every day a double-digit number of answers that are not exactly correct or that have shortcomings. So, my advice would be that if you see a question was well asked, take your time and read everything. If one cannot figure out what the correct answer should be, and why, based on the entire discussion, one would be better off changing professions.
Not voting comes with extra political reasoning about how the "likes"/positive votes/&c. are calculated. They are not weighted in any shape or form. Numbers/masses make nothing right or wrong to boot. There is a high chance people being massively right on a common question but rare to none of some specifics, if the best case there will be an external article topic that might have been read and stating some 'facts' people follow. It does not make it inherently correct.
Voting has become the norm on many websites, and society as a whole, but I fail to embrace it. If I believe something is useful, I prefer to be more human and chime in with some words.
There is more to say on this subject, but this post is long enough and probably reading-unfriendly, regardless of my intent to make it parsable.
Extra bonus for not voting: it reduces energy consumption and saves green trees/oil/uranium, whatever :D
Thanks and cheers!
(Ah, and yes, community wiki is an awesome option, it reduces the flux of positive reputation on the site)