In early web days, back links didn't exist so this was an easy question to answer,, well, it never got asked! The last 4-5 years have seen back links take on enormous weight, which lead to link farms, and link buying. Depending on who you are, this was either good or bad.
Today, Google takes a very dim view of either of these practices, and regularly penalizes sites caught doing it - even if they did it a few years ago. So it's not uncommon to receive "link removal" requests from webmasters or SEO people in an attempt to get into Google's good graces again.
So, does this mean that all back links are bad? No, but you need to be careful where they're coming from and how. If your site had 5 backlinks yesterday, but today has 500, Google is going to smell a rat. It's about a natural progression. That sort of growth is not natural and smacks of buying or farms. But are back links the be-all and end-all? What about content?
Content v Back Links
Whilst it's true that Google has been shifting some weight away from back links recently, they're anything but dead. However, they have diminished in weight as Google tries to focus more on the delivery of quality content. In a recent video, Max Cutts confirmed this fact, while saying that back links still have lots of life in them yet. However, he did indicate the subtle shift towards authoritative authors and authoritative articles.
To quote Cutts...
In general, that sort of reverts back to the way search engines were before links. You’re pretty much judging based on the text on the page at that point. So, Google has a lot of stuff to sort of say the first time we see the word on the page count a little more, the next time a little more, but not a ton more, and then after awhile we say ‘we’ve seen this word, maybe this page is about this topic.’
Quality and value in content
So it's clear that quality content (meaning content not written for the bots, stuffed with keywords) is where this is heading, albeit slowly. When writing, focus on readability for the user, and ask yourself, "Is this giving him or her value?" If not, rewrite it, or don't write it at all. Content should be about value. Quoting large portions of text will get you nowhere with humans or bots. However, as I did above, it's still fine to quote a small snippet or two to get across a point.