The first intuition is to see how many you can get. That's just one piece of the whole backlink pie. Search engines like Google have been around time and have a lot of brilliant minds working for them. A higher quality backlink is worth more towards higher search engine rankings.
Some things to consider about backlinks:
1. Age affects all backlinks. Google specifically weighs a backlink more with age. Backlinks gain in weight over time until after around 6 months they reach their full weight. Basically, it means that the effort you do building backlinks will be worth more and more.
2. Anchor text is hugely important. The words on the backlink itself from the other site also play into it appears the other site views your site. When the keywords you are optimizing for are used, the link gains a much higher quality. The thing to watch out for here is that the text is varying. Google picks up on when all of you backlinks have the same exact text.
3. Getting backlinks from sites with the same theme as yours will benefit you much more than non-relevant sites. This makes sense since a link to your health food site from a car site about old Mustangs isn't going to do much for a visitor, so it won't for Google either.
4. The better the reputation or Page Rank of a site that links to you, the higher quality it is. Fairly obvious. If CNN or Slashdot linked to you, that one backlink would likely outweigh all your other backlinks together.
5. The physical location of a backlink on the page can also be a noteable factor for search engines. Google in particular lends more weight to links the higher towards the top of the page. If there is surrounding content the links appear more natural so they are valued higher.
Reciprocal links are always the hot topic when talking SEO. The truth is, reciprocal links are still alive and going well. Reciprocal links between websites with similar themes is natural and expected. Though I have read many many times of claims that reciprocal linking is dead, rest assured that quality reciprocal links are not going away anytime soon. Google for instance has its sights set on backlinks that were bought, and from link farms where 5 minutes after paying some money you have thousands of sites pointing to yours.
While there are many other factors such as the age of your website and how much content is on your website, those will be left to another article.
Backlinks are indeed the cornerstone of getting a website established on the Internet. Without enough backlinks visitors won't know your site exists, and search engines will put little weight to your website resulting in a further loss of potential traffic, which could make or break your site. The key is to go out knowing what backlinks you want and spend enough time to make your site known. Properly setup, your backlinks will keep your site popular with visitors for a long time to come.
