This question is really broad, but I'll take a crack at it.
There's no universal emotional language of music. Compare, for instance, the writings of Plato on emotional qualities in music (The Republic) to our contemporary genres. Even though we have only vague ideas what his music sounded like, the instruments seem to have sounded roughly like bagpipes, flutes, and harps; yet Plato describes instrumental music as being able to evoke any number of very specific emotions - from military bravado to laziness.
If you listen to traditional joyful music from other cultures, you may be astounded at how dreary it sounds. Celebratory metal music has more in common superficially with Schubert's frantic Erlkonig than one of his Glorias from the same era.
A good way to trace the evolution of emotional ideas in Western music, if you're interested, is to listen to musical theater; check out something like Roman de Fauvel from the 1300s and listen to all the "sad" text pieces you can find, working your way through history. Then do the same with "happy" music. I find it difficult to determine the mood of very old music without the text, but it was apparently obvious to the hearer.
Even with the cultural specificity of music, composers have a mood in mind when they write. Interpretive markings are used to make this more clear to the performer, and, hopefully, to the listener. Ideally, composers communicate exactly the emotion they intend for the music to convey. It's usually safe to assume that specific markings by the composer are accurate descriptions of what the composer felt the music said. Whether the music conveys that that to anyone else is another matter.
Sometimes composers aren't as careful about using descriptive markings, or use a common marking that could have a range of meaning. Vivace could be lively or frantic, for example. Generally though, interpretation should take into account every piece of information the composer gives you.
It may be impossible for a particular listener to hear a particular piece the way the composer intended at a particular time. But it is the job of the musician to attempt to bring the listener to a moment of shared experience with the composer, the musician, and the audience.
I personally don't think there is such as emotionless music. I think that the work of the minimalists in this area is a great demonstration. Even the most sparse music takes us through time, and as emotional creatures we experience emotions during that time. Very barebones music might evoke wildly different responses since it's out of our normal frame of reference, but it will still evoke an emotional transition or response. Favorite examples: Reich's Pieces of Wood and Piano Phase.