I got my first taste from buying sidewalk CD's with emulators and ROMS in it since emulation wasn't well known then. The best part was when it was arcade games, games I wished I could own myself but too expensive to buy a PCB, monitor and joystick. Super Street Fighter 2 Turbo was my most wished game but it was only available on 3d0 and I could never buy a system for one game only. I sorely wished it got a release for the SNES but nope. Being able to play the real game on my computer was only the beginning.
The second best part I discovered about emulation was save states. I realized that even if I had the arcade version of Super Street Fighter 2 Turbo, I would still have to fulfill the requirements to reach Akuma the secret boss to have a fully satisified playthrough and then beat him and if I didn't, he couldn't be continued upon (depending on the version). Which was annoying. But with save states, all I really needed was to reach Akuma once and make a save state before, then I could fight him again and again until I won. I could even play the next day, load my save and fight Akuma right off the bat. I could even make a slew of pre-battle saves against Akuma with every single character. That was when I realized, emulation was in some ways, even better than the actual arcade version.
Which is why I'm annoyed Capcom has nerfed the save states in the new Capcom Fighting Collection 2. You can't save anywhere, only the start of a match and you could only have one save state for the entire collection.