My first EVER encounter with the concept of ROMs and emulators was around 5th grade, 11 years ago. In our country original consoles were a rarity and 99% were NES bootleg spinoffs. I was the only lucky guy with a Gameboy.
Around that time a friend got a SNES from Holland and I became mad over Super Mario World. It was the most awesome game I had played to that date, and as I pouted about whenever I could borrow her SNES and play it, I randomly heard a friend of mine one day talk about playing Mario on his computer. When he mentioned "Iggy's Castle" it became clear what it was. Alas my 486 was too weak to emulate SNES, so I was stuck with carrying the ROM and SNES9X DOS emu with me wherever I went. I only got to play it ONCE on someone else's comp, image was unscaled therefor terribly small. Controls felt awkward yet familiar. It was such an odd feel to be able to play wherever I went a game I once thought playable only on a video console...
The first time I actually got to PLAY a ROM was at the school IT lab 9 years ago, it was POKÉMON BLUE VERSION and it was played on an emulator which I forget, but I remember it was one with mandatory sound support, fixed keys, and a bug where at the start of a battle one of the main trainer's pixel rows would slide across from the OTHER side. I eventually managed to play it on someone else's comp since mine was the same as 2 years ago, and had no sound card. I eventually downloaded RED version aswell and found savegames to be compatible as long as the save wasn't made inside a building(it would then be glitch city). It was also around that time that I discovered Visualboy Advance, which I continued to play them on at that person.
The first time I actually got to PLAY A ROM ON MY OWN COMPUTER was, again Pokémon Red and Blue, 8 years ago. I found a lightweight emulator called "Rew" which also supported savestates and TRIED to emulate GB Link to a point, though always failed at some point. It also supported savestates, which I had first heard about on SNES9X.
My real emulation age began 6 years ago, when I FINALLY got a decent computer, and used VBA for GB and GBA games and SNES9X for SNES games and, 4 years ago, PSX, debuting with Final Fantasy IX.