Mutual trust is a must have in any good relationship, be it romantic, business or just a friendly one. If trust is not present in the relationship, then there will be no future for it to flourish. Usually, at the beginning of any relationship, there is some level of trust because without it both partners won't be able to function normally. As time goes on the trust level can increase or decrease based on action not only of the two partners but also the actions from the people in the surrounding environment that come in contact with the partners.
Because of all that, it is important for two people to nurture a relationship based on trust. The more you can trust each other, the better your experience will be. No one likes to stay in a relationship where jealousy and trust issues are rampant - those kinds of relationships never last for a long.