I’ve been told that all that hand waving is actually crucial to a proper orchestral performance. I’ll buy that, but what exactly then does it sound like when you take him out of the picture? Can they still perform? Is the music noticeably worse?
It depends on a lot of things. If it’s a piece the orchestra’s very familiar with, and the time signatures and rhythm isn’t too complex, the musicians are diligent about following all the volume and stylistic cues, and there are no fermatas (long notes which are cut off on the conductor’s whim), then the performance without a conductor wouldn’t be that noticibly different than if she/he were there. Starting together would be the hardest part, though, even for a well-oiled machine.
But I’ll just tell you it’s weird without a conductor. Sometimes my conductor stops conducting while we rehearse, and it just feels wrong. If one section misses their cue, it can cause other sections to miss their cue. And it’s easy for people (violins usually*) to rush the tempo, which then causes everyone to rush. A conductor is good about holding the group together.
*Violins mess everyone up. They are the bane of the orchestra.
No, he isn’t critical, and usually the First Trumpet or someone just starts leading by example.
What he is very critical for is rehearsal, where he gets the band to play the peice exactly right and exactly his way. Once they have rehearsed it that way many times, he is more or less done. This is why they can bring on a “guest conductor” without them botching up the piece.
It takes a skilled artist and craftsman (not to mention a dictator and diplomat) to get an orchestra playing a piece “just right”. After that, you can have a monkey up there waving the stick.
In high school we had a Spring Musical every year. In one evening performance the orchestra director was over talking to someone and completely spaced out the cue for the orchestra to start.
We did it anyway. Without him. And perfectly, I might add.
But they are about a third the size of a full orchestra, so I expect that there would be less need for a condutor.
Sit me on fifth desk, I’ll slow things back down for you 
I watched Andre Previn give a demonstration on a TV program, where (if i remember correctly), he started the orchestra off, then sat down. They carried on (but of course they were a professional outfit and had rehearsed the piece).
Also sprach Zarathustra by the Portsmouth Symphonia [RealAudio].
As a violinist, I can say that this is true. And there are three main reasons for it:
(1) The sound of the violin is the “base” sound of the music and if the violins go wrong, it’s just wrong.
(2) There are more violins than there are anything else, so it’s a lot harder to keep them together.
(3) The violin is harder to play than most other instruments in the orchestra and on the average in non-professional orchestras, the violins are at a lower level of proficiency with their instruments than the other musicians. In many amateur orchestras, the violinists simply suck and one must rely on the woodwinds and the brass to carry things along.
Given all that, the concert master (principal first violinist) fills in when there’s no conductor. So he or she gives the cue for everyone to start on time. Beyond that though, it’s not easy for a seated, playing musician to give all the cues that a conductor would.
I remember once playing Pachelbel’s Canon in a junior string orchestra in which the stage started empty except for the basses. Then the cellos came on, then the violas, etc. The conductor came on stage last only to give the final end cue. That was very difficult to pull off.
I maintain the opinion that any performance of a work by Schoenberg would be vastly improved by the absence of a conductor.
And if that doesn’t stop it from being played, take out the string players one by one until they all get the message.
It was said earlier in this thread that a lot of the conductor’s work is done at rehearsals, and having played in a few emsembles in my day, I’d say that’s true enough. So in spite of the fact that the conductor might be able to be removed for the performance, it’s probably not something you want to do during rehearsals. A conductor should be there, especially for rehearsals.
But there has been at least one conductorless orchestra: the Pervyi Simfonicheskii Ansambl (“First Symphonic Ensemble”), which was organized in Moscow in 1922. The “Persimfans,” as it was known for short, wanted to show that the egalitarian ideas of Karl Marx could be put to use in an orchestra too. From the link:
So it could be done, but it was a lot of work for the musicians.
The conductor is a relatively recent invention. In Mozart’s time, for example, there were no conductors (the scenes of Mozart conducting in Amadeus were anachronistic). I believe, as others have said, that one of the musicians (probably the first violinist) would take the lead.
I’m strongly tempted to steal this idea 
Please do. It was great fun. (I doubt it was entirely novel anyway.) Actually, I think it went even slower than that, with only one or two musicians coming on at a time. Someone was assigned to shoving people onstage at appropriate intervals.
The Symphony of the Air played without conductor [for some time] after Toscanini’s death.
What does an orchestra sound like without a conductor?
Less tapping.
Bet the cellists will still hate it, though. Pachelbel Rant
*** Ponder
Very nice. Has anyone compiled a list of the pieces that he references in his rant? I’m sure I heard U2 in there. What else?
Yes. I agree with everything you say. Are you a music instructor? You’ve hit the nail on the head with everything you’ve said. One thing, the concertmaster will stand up and start the orchestra and occasionally stand up to guide through difficult passages.