First, there really isn't a solid tradition of performing ensemble music from memory. One might consider concertos, but, then again, the orchestra isn't playing from memory. There is, very interestingly, a newer tradition of some classical ensembles, particularly in the early music world, performing from memory, but these seem to be anomalies. In some choral singing, there is a memorized tradition, particularly among children's choirs. The Philippine Madrigal Singers, a top-notch adult ensemble, perform from memory--and, I should add, seated and without a conductor.
Because I play chamber music with a variety of people, often playing the same pieces with different ensembles, I think that playing without music would be quite disadvantageous. I'm not suggesting that a memorized piece is a "learned" performance of that piece, but, in chamber music, we often need to mark up our parts as interpretive decisions are made. Keeping track of all of those decisions would be very difficult and could be disastrous in performance--and I'm not even referring to score-based memory lapses. I'm not saying that it's impossible, but, for me, memory work takes a lot of my time, and I'm not at the point in my career or interest where I want to devote that much time to my ensemble players. Were I a string player in a permanent string quartet, however, I think that playing the great quartet repertoire from memory with excellent colleagues would be a wonderful!
In the case of contemporary music, it's quite common to perform from score. Not only is the repertoire often hot off the presses with composers revising to the very last minute, non-tonal music can be wickedly difficult to commit to memory. More so, some contemporary composers don't expect their music to be played by heart.
Composer Larry Bell left this comment on an earlier post:
There is a book by (the late) Charles Rosen about Elliott Carter's piano music. At the time the book was written, Mr. Carter had not written very much piano music, so the book is a thin one and fundamentally about the one and only Piano Sonata (ca. 1945).
At any rate, even in the 1950's Carter had a reputation as a composer who wrote difficult music. Rosen, showing himself to be a progressive pianist, took on the Carter sonata and played it many, many times from memory.
Once, when in the wings at Coolidge auditorium at the Library of Congress waiting to go on stage to play the Carter, a stage hand asked Mr. Rosen what piece it was that he was about to play. When Rosen replied the "Carter Sonata," the stage hand said, "Oh, that is a very difficult work."
The concert was somewhat of a disaster, and from that time onwards Rosen was never again able to play the Carter Sonata from memory.
While this list of reasons why one shouldn't memorize is far from complete, I'll leave this final suggestion: One should not play from memory if a piece isn't learned well enough. Let's face it, we're all busy people, and we simply may not have enough time to commit a piece to memory. But this should not be the norm. We need to make more time for our practice, even if it means that we'll be performing a little less often.
And, as I've already suggested, working towards memory isn't just about the audience, it's also about our own musical development.