I had no idea retargeting even was a thing, until one particular ad kept repeatedly showing up.
When my grandmother died last year we looked up the website for a cremation service to find their phone number. Then for the next week or so I kept seeing banner ads for the same cremation service all over the web, on completely unrelated sites.
I would expect to see a cremation service ad on an obituary page, maybe a local newspaper, etc. I would not expect to see it on, say, a tech blog or an Android user forum. And I could consistently refresh threads on that forum and keep seeing that particular ad from that same company. Maybe it was the nature of the service advertised and my frame of mind at the time I was seeing it, but I was really creeped out.
I cleared cookies and it stopped. At that point I realized that the advertiser was doing something in particular to tell Google that I visited their site and to start throwing ads at me elsewhere. I checked out the AdWords docs to see how they were doing this and figure out how to opt out.
I don't know how long this has been a service offered by Google. Up until that one instance I likely had countless ads retargeted at me, and I may have even clicked such ads. And it works great until one instance where I'm creeped the heck out and I push back.