My rarest collector's item is the Guardian-Vexor, so precious that I keep it on a separate character that I haven't logged into for years, just to avoid the temptation to undock it. According to my sources, only 12 of the original 50 ships remain in the entire game.
The story of how I acquired it is rather boring.
I started a new character from scratch in mid-2004 as a Yulai trade alt, aiming to demonstrate to a friend that knowledge is the most valuable asset in EVE. After completing the initial 10 "tutorial" mission chain, I found myself with a few ISK in the Alentene system. There, I joined a random production corp and began semi-afk jetcan-mining career with a Velator, selling ore to my corp mates. The next day, they lent me an Exequror, which boasted 4 turret slots and a base cargo of 600m3 (I still remember these details vividly).
My initial goal was to earn 4.5 million ISK for a Vexor hull, but then I spotted a modified Guardian-Vexor on the market for 16 million ISK. This version had a missile launcher hardpoint, and I knew that with a Rapid Light Missile Launcher filled with defenders, I could effectively combat missile-wielding rats. So, I decided to mine an extra day and purchase the Guardian-Vexor for mission running. So I did.
Fortunately, I quickly progressed to battleship-class ships, sparing my Guardian-Vexor from an explosion. It remains docked in a secret station, unlikely to see the stars again, which is a bit saddening.