Let me share my thoughts with you about this issue. We have been collecting different attributes of what we mean by "trust". Summarizing (more or less) :

• Clint: To rely on someone as well as a sense of predictability in the behaviour (to do what you say you are going to do). It's also to take care of the others.
• Esko: The quality of the relationship. Feeling respect and reciprocity
• Marcus: The basis of many relationships. To understand each other (especially between cultures). He also addressed how you can feel trust.
• Sabine: A basic ingredient. It arises from the character: reputation, willingness, presence. To give a chance.
• Tentim: Trust is built from a common goal or ground to start with.
• Adele: It comes from history, looking backwards, after reflection. "An intention to allow a state to develop"
• Minjuan: Belief, faith, to openly share yourself. To share your goals. There are different levels of trust
• Diego: Nemawashi. To develop a shared understanding as a scaffold.
• Me: A gut feeling. Confidence and predictablity. Physical and ethical dimensions.

Up to a certain extent it seems there are two big dimensions in our definition of trust: what I called "affective" (how we feel) and what I called "competence" (how we do). When I read all the answers I had the feeling of having dealt with this issue before. I reviewed my handbook of social psychology and I found that it seems that people distinguish easily between social-affective competence and intelectual-performance competence for socially valuable values. Further, it seems that the most valued features among people are: sincerity, honesty, understanding, loyal and trustworthy which, in my opinion, fit quite well with our definition of trust. (Lydon: "Interpersonal similarity and the social and intellectual dimensions of first impressions" Social Cognition 6, 269 - 286)

I dug a little bit more to find out why. A possible explanation comes from the implicit personality theory (IPT). IPTs are the beliefs we have about which people's features or characteristics happen together (for instance, quiet people are timid).