I'm starting wih the first game, reading up, getting my party composition together. I noticed the split party option, are there any quests that this is necessary or useful, or do you usually keep your party together for everything?

If I remember correctly experience is always split by the number of characters, so splitting your party would allow you to level up one char faster if you want.
Also there are parts in some games you can only solve if you split your party.

And its useful for some traps if you got some party members that are too clumsy.

It's only necessary a few times in the series that I remember. I'm currently playing Shadows over Riva and just completed a section where this was required to complete an area. I remember something similar in Star Trail.

It can also be optionally used if one or more of your party's stats are keeping you from succeeding at something.