To musicians, nothing is more important than intonation. It should be the one thing in the back of our mind at all times...
As a string player, we should be hypersensitive to our intonation. No one plays perfectly in tune - I don't, my students don't, Yo-Yo Ma doesn't. What we're after isn't perfection, but rather a finely developed ear and quick reflexes so we can adjust before our audience hears something they don't like.
One of my favorite ways to work on intonation with students - once they get to an appropriate level of technique - is by using chords and double stops. Here we are working on the ending of Musette and trying to fine tune our left hand notes so it sounds very beautiful!