Possibly the largest affiliate network would be Amazon Associates. You sign up for an AA account, and you share your affiliate link for products with other people. If you do it casually (e.g. just recommending to friends and family on FB), then you can get some extra pocket change. If you do it professionally (e.g. actually finding a niche, doing market research, building a website w/ a capture page, etc), then you really need to work on promoting the products, which can be a full-time job in itself.

Of course, Amazon doesn't rely on its affiliate program to be big, but that's also what's great about being an Amazon affiliate--you don't really need to "sell" since everyone knows Amazon.

I can't think of any legit affiliate websites off the top of my head, but just imagine a site about dog training (a very popular affiliate niche). It has some free content on how to effectively train your dog (which could be valid or invalid), and in the content are some affiliate links. If the content is actually valid, and it works, and it's actually good content, I don't see how putting affiliate links on the article is spammy. I always appreciate it when a blog post links to a product it mentions because it saves me from having to Google it (but I will anyway to get a best price).

Of course, you can have complete spammy people, who have fake websites with false content (or crappily outsourced content) and comment random people's blogs for link bait, and unfortunately that's a practice that some "mega affiliates" promote in their "how i became a rockstar affiliate" products, but it's not fair to judge affiliate marketing as an industry based on a few bad eggs, no matter how numerous they may be.