Progression systems in video games are not something exclusive to RPGs but it is certainly one of the genre's defining features. While twitch game genres like fighting games, shoot 'em ups, and rhythm games develop the player's reaction time, RPGs have progression systems that develop the player's character or avatar. Unfortunately, most RPG progression systems don't make the player feel stronger in any meaningful way and instead have arbitrary numbers that increase as you level up. An engaging progression system has avatar growth that significantly affects how the game is played and has a level of customization that allows the player to decide how their avatar grows.
Mega Man Battle Network is an RPG series that manages to have significant avatar growth without even having experience points! Instead, the avatar growth in Mega Man Battle Network is driven by power-ups that the player can obtain through exploration, shopping, and side quests. These power-ups increase the strength of the titular character, Mega Man by upgrading health, attack power, fire rate, and charge speed. What makes each power-up significant is how just one can substantially boost Mega Man's ability in combat. Mega Man Battle Network even assigns a level to Mega Man based on how much power-ups you have equipped so that players can track their progress. However, the most interesting example of significant avatar growth in the Mega Man Battle Network series "style change" didn't appear until its sequel. A style change is an upgrade Mega Man receives partway through the game that grants him an element affinity, a new stronger "mega buster," and a passive ability like "super armor" (the ability to take damage without flinching). The style change Mega Man receives is determined by what strategies the player uses in battle.
This is not to say that RPGs with experience point progression systems are all bad. In fact, one of the best progression systems can be found in Paper Mario. Aside from the ingenious way that leveling up is always done by acquiring 100 "star points" (experience points) which makes progress easy to track, upon gaining a level Paper Mario allows the player to choose how Mario grows. The three stats players can choose to upgrade are "heart points" (health), "flower points" (mana), and "badge points" which increase the amount of passive or active abilities Mario can equip. What makes this progression system engaging is how the player can craft their own experience by choosing what stats to upgrade, especially because neglecting the health stat can serve as a kind of pseudo-hard mode. Custom growth isn't only limited to Mario but also applies to his party members or partners as they are referred to in Paper Mario. Partners can be upgraded using a "super block" which boosts their attack power and grants them a new attack. However, a super block can only be used once so it's up to the player to choose which partners to upgrade.
Of course, both of these RPGs include elements of significant and custom avatar growth in their progression systems which is why they are among my favorites. One thing I would like to see RPGs experiment with more is progression systems that are driven by the narrative. Examples of this include the Magicant section in Earthbound that has Ness face his inner demons to get stronger and how the bonds with your party members determine the strength of Persona you can create in Persona 4. A progression system that is solely driven by the narrative would ensure that there would be no ludo-narrative dissonance or instances where the narrative and the gameplay come into conflict with each other.