October 29th, 2003. I only remember the exact date because it was also my 18th birthday. I got started pretty late at night (had to go out to Gamestop and get the game when my parents got home from work, then install, get account set up, and download updates), so I didn't get to do much (since I had school the next day). I spent about an hour just learning the controls and how to do basic things. I specifically remember being frustrated at not knowing how to open doors; it took quite awhile for it occur to me to target them and click on them. In my defense, at the time I don't think I had discovered that you could scroll through targets with tab or 0 on the number pad; I think I was just running around hitting enter, which of course just targets the first thing that tab would have.
Anyway, the most memorable part was my first time leaving town. I zoned out, and immediately got killed by a Goblin Thug who someone had just zoned (yes, back in the day, mobs didn't just depop when zoned), before I could even do anything. I was more amused than angry. Then a level 70 SMN/WHM (level 70 being the cap at that time) happened to zone out just as I died, and he raised me. That was pretty cool.
Seeing as I started in the middle of the Halloween event, I remember being confused when NPCs were suddenly normal people again, rather than being in Shadow and Skeleton costumes and such. I also remember the point when, probably at least a month and a half, if not two months or more after I started, the Valeriano troupe disappeared from Windurst Woods. I thought they just weren't loading for me, and zoned and came back and they were still gone. I eventually learned they move to whatever nation is in 1st: Windurst had just been in 1st place for months straight. XD I definitely had (and still have, to an extent) a lot of Windurstian pride. :3
I was also around level 9 or so when I remembered (or was reminded; I had read about it but forgotten) there was an Auction House, and decided to check it out. Boy, I felt stupid for trying to make money by selling things to NPC. ("Wow, Silk Thread sells for 200 gil/piece! That's way better than all this other stuff!")
It took me forever to figure out how to craft, too. It never occured to me to use the crystal as an item. XD I remember getting so frustrated before finally just asking someone who I saw crafting stuff.