Generally speaking, I hold the opinion that improving is always better than reinventing. Only when a brick wall is hit, can reinvention be done and is actually purposeful. Before that - and, if it is applied only once - it is merely a novelty, doomed to fade with the passage of time.
For example, random encounters. A lot of people dislike them, and I can see where they come from. But, as games like Bravely Default have proven, they don't turn out to be so bad once you are allowed to set them to your wants and needs. Which is why, as of right now, I do like random encounters, provided they can be manipulated.
Another example would be the "level up alternative". Now, this is mostly pertaining to the way this was done in FF VIII, X, XIII and XIII-2 - if we're talking these games, my stance is a firm "good riddance to this rubbish". But, again, if done right, this can enhance the experience. If I may indulge in some mild hype of a game I backed via crowdfunding, the upcoming Indivisible has mostly replaced the traditional level-up with items the player can find while exploring, an addition birthed from the metroidvania DNA the creators decided to infuse the game with. This - or, to provide another example, the level system used in the Souls franchise - is something I can appreciate, largely because I get the feeling that the designers thought about every aspect of their game.
If there's things I straight-up want to see gone: No direct control over other party members (at least let me have them use items, ffs); failure/game over when party leader falls (just... just... AAAARGH); level caps (again, something that can be handled well but is usually just an annoyance); pretty much the insertion of mechanics/systems from other genres just because they happen to be popular (REALLY not looking forward to FF XVI if it has survival and crafting stuff*).
*I so hope this is just a jest.