I also don't mind random battles too much. I have yet to encounter a game in which random battles are entirely meaningless, but nothing compares to Final Fantasy Legend II on the Game Boy. Battles actually meant something in that one.
Treasure Hunter G is a great SNES game that doesn't feature random battles. I think it was the last RPG Square published for the SNES; a translation patch is available. (Actually, aside from the awesome battle system and nice graphics, the rest of the game is kind of dull and linear, but the battle system makes up for it.)
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