The one that comes to my mind immediately was when someone contacted me and asked my opinion on why their traffic dropped drastically. I asked them if they recently changed or updated their website and they said yes. I did some quick checking and found a bunch of now-dead links. After I set up 301 redirects to the correct pages his traffic came back up. After that, he hired me to market his website.
Another way is to post an answer or provide a tool on your website about no one else has then let people know about it in forums and social media. This is what I call self-replicating links. Where you provide something and people share it and link to it as it gets more popular.
· Answer requested by Brant Broyn