My favorite is my personal domain. I originally registered it through the "Yahoo Personal Address" service, and the email was hosted through Yahoo. Later, they retired the "Personal Address" service, and changed to two separate services - one for businesses, one for personal use. My account got grandfathered in badly - I was apparently in neither the new small business nor the new personal service. I later attempted to change something about the domain registration (I wanted to host a website that wasn't on GeoCities,) and nobody could help me. The small business side theoretically would have allowed me to, but they swore I was a personal account. The personal account side said they had no record of me. After much back-and-forth, I registered a different domain, and figured I'd just transfer the Yahoo domain. Nope, couldn't transfer the Yahoo domain because I couldn't get the transfer key. I figured I'd wait for it to expire and snap it up.
Nope, a squatter got it before me.
The domain was my last name dot org. (The dot com was held by a distant cousin, who ironically later lost THAT to a squatter himself.) My last name is not common (in the entire world, there are maybe three-four dozen of us.) It is not famous. It is not "trendy" or "interesting" in any way. There is no comprehensible reason for a domain squatter to want it.
When I followed the "make an offer on this domain" nonsense, I was forced to enter a minimum offer of €200. Fine, whatever. I entered my €200 offer. It was rejected, with a counter-offer of €10,000 (obviously automated.) BS. The automated system wouldn't let me "counter-counter" offer for less than €1000. Not going to do that (they claim it would be a binding offer.) I have a recurring alarm set every year for its supposed expiration. They have never let go of it, for over 7 years now. Every year, I check to see if it's the same squatter. It still is. I've attempted to find a way to contact a live human at the squatter to let them know that they've wasted their domain registration money every year - and that I'd offer them double what they've spent on registering it every year - but I've never been able to find a way to contact a live human.
And, now that I've thought about it, I decided to check again (the expiration has always been June) and the dot com my distant cousin lost is still held by the squatter, but apparently that same cousin managed to get the dot org! (Hrm, did I forget to check last year? Now that I think about it, I may have...)