As other people said, it's best to have them on the same character. And usually there are cross-class skills you nearly need at higher level.

For example a tank will need stoneskin which is conjurer 34, a healer will need swiftcast (THM 24 I think), the BLM will need quelling strikes from Archer, eye for an eye is very good for healers, mantra for melée DPS, etc. Most times there is a cross-class skill you need from a class you still haven't leveled up yet.