Actually, my first ES experience was way back in 2001, and I did not actually game that day, I merely watched somebody
else as he gamed. Let's go back to the moment, shall we? (insert sappy music here).
The Xbox was new and I was at a party with this person I was dating. I was a gamer back then, but had a Playstation instead of an Xbox. I was very much into Tomb Raider. Anyways, I'm at this party and there's this guy playing a game on the TV. I was immediately drawn to it. It looked like a medieval fantasy game, which I had seen before on Playstation, only diff was THIS medieval fantasy game seemed not to have any 'boundaries.' I was so used to playing games which are very linear, with very few options for exploration, you see. Well, THIS game seemed limitless. The onscreen character ran up to some sort of giant wall (a town or a castle) and the guy playing the game began exploring all over the place.
That's one thing I noticed: there didn't seem to be any boundaries in this game. There was no 'YOU CAN'T GO HERE' message. I remember there was a lot of fog in the air, too.
Knowing the way I am, I probably asked the guy what the name of this game is. His answer would have been Elder Scrolls III: Morrowind which is a pretty odd name for a game. I have a terrible memory, and wouldn't have remembered such a name, but I probably assumed that if I searched the stores I'd find it for Playstation in no time. And I DO remember searching for it. I bought lots of fantasy games for PS in the next few years, searching in vain for the open-world game I saw at that long-ago party. Since TES: 3 was not on PS, this means I had no idea that my efforts were in vain.
So that's actually my first ESE, folks.

I wouldn't actually play in ES game until seven years later, and I'll post what I remember from that experience later.