It depends on the requirements of the music,
For pieces such as Vivaldi's spring (cited in @msh210's comment) that are closer to chamber music than orchestral music, conductors are not mandatory. School ensembles will have small orchestras playing thoses pieces with a conductor, so that all can be together, professional recording seldomly do because they do not really need it.
For music such as concertos where there is a solist, good ensemble can rely on their ears to play with the solist. Great musicians often play concertos without a conductor, but as for real advantages, I feel it's a bit for the show. Having a conductor is tighter then not.
Now pieces such as Mahler symphonies or contemporary very complicated music won't be played without a conductor. Well I've never seen it, I'd be happy to, but that repertoire tends to have lots of voices, never beginning to play together, necessiting cues.
That is without considering the position of the conductor, which can actually hear the global result of the orchestra and adjust dynamics (how much noise, so to speak) dynamically (no pun intended), which one can not do while playing some complicated solo violin partition and leading his/her section.