Many RPGs have different ways of handling how encounters with enemies start. The most common is what we see in Phantasy Star: wander around until you're suddenly pulled into a random encounter. Another common option is scripted encounters, like in Chrono Trigger: the enemies always appear at certain places. Some games have monsters walking around the screen; you can dodge them or run into them for a fight. And there's probably other ways I've forgotten at the moment.
What game, or games, do you think take the best approach to starting up enemy encounters?