There are a number of ways in which cats show affection and trust, and not all of them are as immediately obvious as curling up into your lap and purring.

Blinking:  If they feel threatened or uncomfortable, a cat will do its level best to keep its eyes open.  Blinking, or half-closed eyes are a sign of trust.

Grooming:  If a cat allows you to groom it, and even more if it grooms you, this is a sign of acceptance and trust.  Cats use mutual grooming for stress relief and relationship building.

Head Rubbing:  This is a combination affection and mark of ownership.  Cats have scent glands on their faces, and when they rub their head against you, they are marking you as their own.

Stomach Display:  This is one of the deepest signs of trust a cat can give.  However, presenting the stomach does not necessarily mean asking for belly skritches.  Depending on the cat, trying to do anything to the belly, even if presented, will provoke a defensive response, no matter how much they like you.