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If I would suggest one series that comes close to perfecting random encounters, its Wild Arms, specifically Wild Arms 2nd Ignition as it allows you to choose whether you want to fight or not as long as your levels are high which makes the most annoying aspect of random encounters a thing of the past, by which I mean,
This makes me think of Earthbound. In that game the enemies appear on the over world map, and touching them causes you to enter a battle screen. If you are strong enough all touching them does is cause you to gain experience and items from killing them, just a dialog box that pops up on the bottom. You don't even have to close the dialog box, just keep running through the area.