Let’s start with what Google says. In a nutshell, it considers links to be like votes. In addition, it considers that some votes are more important than others. PageRank is Google’s system of counting link votes and determining which pages are most important based on them. These scores are then used along with many other things to determine if a page will rank well in a search.
You can confer some of your site's reputation to another site when your site links to it. Sometimes users can take advantage of this by adding links to their own site in your comment sections or message boards. Or sometimes you might mention a site in a negative way and don't want to confer any of your reputation upon it. For example, imagine that you're writing a blog post on the topic of comment spamming and you want to call out a site that recently comment spammed your blog. You want to warn others of the site, so you include the link to it in your content; however, you certainly don't want to give the site some of your reputation from your link. This would be a good time to use nofollow.
Totally agree — more does not always equal better. Google takes a sort of ‘Birds of a Feather’ approach when analyzing inbound links, so it’s really all about associating yourself (via inbound links) with websites Google deems high quality and trustworthy so that Google deems YOUR web page high quality and trustworthy. As you mentioned, trying to cut corners, buy links, do one-for-one trades, or otherwise game/manipulate the system never works. The algorithm is too smart.
Do you regularly publish helpful, useful articles, videos or other types of media that are popular and well produced? Do you write for actual human beings rather than the search engine itself? Well, you should. Latest research from Searchmetrics on ranking factors indicates that Google is moving further towards longer-form content that understands a visitor’s intention as a whole, instead of using keywords based on popular search queries to create content.
A breadcrumb is a row of internal links at the top or bottom of the page that allows visitors to quickly navigate back to a previous section or the root page. Many breadcrumbs have the most general page (usually the root page) as the first, leftmost link and list the more specific sections out to the right. We recommend using breadcrumb structured data markup28 when showing breadcrumbs.