Pokemon is one example of how a game can barely change at all, and honestly have almost no story either, and still be successful. Because it has another kind of fun to it.
I personally don't like Pokemon, but I can understand to some degree. It has a simplicity, a simple no non-sense battle system, and then they expand it all times 700+ monsters to collect, 3x3 teams, personalities, evolution, breeding, and what not.
Dragon Quest on the other hand barely changed at all. Sure they added a job system in certain games (DQ6, DQ7, DQ9), monsters to make your team (DQ5, DQM series), skill points (DQ8), characters locked in their tasks (DQ2-3-4), but the battle system has very little evolution. They added tension, separated skills of spells at times, but overall it all worked the same : Fight, Item, Run.
Final Fantasy on the other hand ALWAYS was change evolution and changing. You can list what was different between each games to see it on your own. I think that is the defining trait of the series, and the reason why it kept on top of gamer's interests. FF is somewhat more popular in EU and US probably for that reason, while DQ is king in JP.
Here's an example of the changes between the games :
FF1 was made to 'compete' with other RPGs at the same, like Dragon Quest. The idea was to make a game that would be different. It was the first game that let you see your characters and attacks, even seeing the weapons with different graphics when you change it. DQ3 somewhat used a similar job system later on, but FF did it first.
FF2 added chocobos, the now staple Cid, changed the exp/level system to a grow by use system. The first game to use MP for spells as well if not mistaken. There was no 'tiers' of spells (Cure 1-2-3), rather a single spell that would just grow in power by use.
FF3 went back to the jobs system of the original and expanded it immensely, and allowed you to switch jobs. Also the first game with summons. Where FF1's jobs only had stat and spell casting differences, the jobs this time introduced skills as well, such as Steal for Thief.
FF4 had the most extensive storytelling yet, with characters locked in their jobs, but there was various features that were, and still is, unique to the series, such as the Golbez fight in the dwarf kingdom. How many fights can you think about that have you start the fight on the defensive like that, even if you used the inn and saved before? Also the first version of the ATB.
FF5's story was somewhat less stellar than FF4, but vastly improved FF3's job system with support jobs. The first game with Moogles, and one of the biggest FF world yet with 3 different overworlds. Also the overworld sprites had more expressions than FF4, and weren't limited to 'looking down' at the screen to make them (watch Palom knocking Porom, always looking down).
FF6 pushed the SNES to the outmost, the first game that had the same sprites in and out of battles (rather than the smaller overworld version used before), and had the biggest palette of expression yet, as well as the largest cast of playable characters of any FF game yet. The first game to have 'limits breaks', where it was a 25% chance of making a special attack when in low health. Also the first time that spells were learned not by levels or buying them, but rather by teaching them with the magicites. Characters also have 'skills' related to their class, but magic is not tied to it.
FF7 was the first step into the 3D world, but outside of that, expanded more on FF6's system. All characters can use magic, but limited by the materia system, as to how many you can equip. Also highly customizable as a result of combining materias for effects, such as elemental attacks. Probably, with FF9, the game with the highest amount of 'mini-games' involved (not necessarily as side-quests, like keeping warm in the ice mountain).
FF8 improved the graphic system, but also changed alot of details : Levels end at 100 rather than 99, monsters rise in levels and power with you, magic has limited uses, but limited by the amount you can find or draw out of monsters, monsters offer no gil reward, there is practically no chests, weapons are upgraded through finding items from monsters or trading cards.. LOTS of changes, more than I can list here.
FF9 going back to the roots voluntarly, characters that have set jobs and tasks like in FF4, on top of being stuff with more references to earlier games than you can shake a stick at. The spell and skill system similar to FF6, but not limited to magicite, but any equipment instead, and also limited by how many you can equip, which further cutomizes your gameplay to your tastes or needs for bosses.
FF10's ATB was changed to be more tactical. No more leevls, the characters are set in their own classes only for a part of the game, as later they can spill into other paths. Also spellcasting not limited by MP, it rather affects how much time it will take for the character's turn to come back around, making you think your actions on a new level.
This is just the short version of course, you could go on forever. I'm stopping at FF10 as well, but there'd be lots to say about 11 to 14!
