Of everything I did on my Silver cartridge, nothing was more memorable than my first meeting with Raikou.
I was walking in the grass just outside Cherrygrove, for what reason I don't remember anymore, when an encounter was sprung upon me and I was suddenly face to face with the legendary Raikou! I never pass up the opportunity to catch something new, so I engaged in combat using my only decently leveled Pokemon, my level 34-ish Croconaw. For some reason, the Raikou didn't run, but fought right back, and I managed to get it in the red before tossing an Ultra Ball at it. It was only after it escaped that capture attempt that the creature fled.
I haven't heard anything similar happening to anyone else since then. Perhaps my game glitched? Or perhaps I was chosen by Raikou, haha. I continued to track it down for a long time afterward, but I never caught it (nor Entei and Suicune, though I tried, dammit!) before my internal battery died and everything was gone. :'(