Vagrant Story comes to mind right away as a game that has no levels at all. You increase your stats mostly by finding items (e.g., "Elixir of Mages" boosts your magic) and also by receiving bonuses (e.g. Strength + 1) from defeating bosses.
SMT III Nocturne, which I'm playing right now, does have numerical levels, but gaining a level doesn't boost your stats overall; instead, it gives you a point that you can put in one of five different stats. If you don't allocate points to a stat, it never increases. That sounds somewhat like what you're interested in. Moreover, in SMT III, leveling up doesn't increase your stats that much. In most cases, the best way to advance your party is by combining your demons (party members) to form new, stronger demons instead of leveling up the ones you already have.
The Mario RPGs use a similar system where leveling up only gives you a point to put in one stat. (I don't know for sure about Paper Mario 2 - I haven't played it yet - but I'm assuming it's the same.)