Cloud computing is revealing a new scenario where different cloud customers need to collaborate to meet client demands. The cloud stack must be able to support this situation by enabling collaborative agreements between cloud customers. However, these collaborations entail new security risks since participating entities should trust each other to share a set of resources. The management of trust relationships in the cloud is gaining importance as a key element to establish a secure environment where entities are given full control in the definition of which particular services or resources they are willing to share. Entities can cooperate at different levels of trust, according to their willingness of sharing information. This paper analyses these collaboration agreements defining a taxonomy of different levels of trust relationships among customers for the cloud. Privacy concerns, assumed risk, as well as easiness in the definition of the trust relationships have been taken into account. A set of different trust relationships have been identified and modeled, enabling entities to control the information they share with others in the cloud. The proposed model has been validated with a prototypical implementation. Likewise, some examples to illustrate the application of these trust models to common cloud collaboration scenarios are provided.