This is the most common sign of cat love. If your cat purrs when he is around you, it is obvious that he loves you. Purring also has health benefits. It lowers your cat's heart rate and also makes you feel more calm.
The technical term is "bunting". It's whenever a cat touches you with their head or cheeks. Cats have scent glands on their cheeks, if they headbutt you, it's their way of marking you with their scent. This is a way for your cat to bond with you. Basically, they are saying that you belong to them.
Cats love to moon those that they love. They are showing that they trust you. Pay close attention to their tail language. A cat communicates through how they carry their tail. If they moon you with their tail held high and a hook at the tip, this is a sign of respect.
Kittens do this with their mother when they are nursing. Grown cats will knead when they are feeling loved and happy. It's a sign of well-being and happiness.
Cats love to scratch! As I wrote in the how to stop cat scratching post, one of the reasons that cats scratch is to express affection. They will usually scratch something they associate with you, like a favourite chair or sofa. There are scent glands on cats paws. Scratching allows them to leave their scent on the furniture. It's another sign of claiming you, like headbutting.
Showing Their Belly
One of my cats does this on a daily basis. Whenever I come home from being away, she rolls on the floor and shows her tummy. This an obvious sign of trust and love, as that's the most vulnerable part of a cat. If she shows you her belly, it's her way of saying that she trusts you. It is also an invitation for playtime and petting.
Grooming or licking is another way that cats show their love. This is your cats way of marking you with their scent. It's a very affectionate cat that does this. They are saying you are part of their family.
Both of my male cats love to give love-bites. It's a sign of playful affection. Usually a cat who likes to lick or groom you will give love-bites when feeling frisky.
Cats only give direct eye contact with people they trust. In the wild, looking an animal directly in the eye is a sign of a challenge. Your cat must trust you if they are making eye contact. If they stare and then blink their eyes, this is a sign of love. Look back into their eyes and blink slowly to return the love.
Ah, every cat owner has received a dead mouse or lizard on the pillow. Your cat is sharing their "gift" with you. It's a sign of love. Best to praise them and dispose of the gift in the trash bin. Some cats will also gift you with one of their toys. Take it as a compliment.