I know my cat loves me because she hasn’t killed me in my sleep. Yet.
Try missing a couple of feeds or sitting in the wrong chair, then check back with us. If you can.
It is not written in a scholarly way, but the various behaviors listed are legit. Rubbing up against you, hanging out with you, allowing you to rub their tummy, etc…
When I come home after work, she’s just inside the door waiting to greet me, grabs my ankle (maybe nips the hem of my pant leg), and rubs her head on the top of my shoe and winds up doing a somersault over my feet. I take this to mean she’s happy to see me.
My Cattius Maximus is a really friendly guy - probably because he’s got a good sized dollop of Maine Coon in his DNA. The minute I open the front door, no matter where he is in the house, I can hear him meowing non-stop as he makes his way toward me. When he arrives, because he is competing with 3 large bouncy dogs for my attention, he’ll jump up on my shoulder where he sits like a parrot, making little chirps in my ear and purring.
I’m pretty darn lucky to have such an affectionate kitty.
He also enjoys sitting on my lap and having a ‘conversation’ with me. He’ll make miscellaneous kitty noises, then look at me for me to respond. When I do, he’ll ‘answer’ with more miscellaneous kitty noises. When he’s done communicating, he’ll curl up and have a lap nap.
I am currently being exfoliated by one of mine. A couple of them greet me at the door and are usually the ones that follow me around (including to the bathroom) They are always sleeping on me or touching me. They are jealous of each other, the phone and the computer. The headbutt, tolerate kissing, play bite … they pretty much do everything on that list.
I can never sit on the potty without a cat on my lap. One of them will come up, turn around a few times and curl up on my lap. I usually grab a magazine from the holder next to the toilet, and sit there for a few minutes, because I don’t want to move the cat. I like it the best in the Winter, since it keeps my legs nice and warm. 
He brings me his toys and puts them by my side of the bed when I’m sleeping.
When I work really late or travel he hangs out near my closed bedroom door and cries like he’s trying to get my attention. (apparently he thinks I’m silently in the room)
I have advanced anemia and spend quite some time flat on my back in bed.
Kitty loves to curl up.
Yesterday, I noticed she had one forepaw under my wrist and the other on top. She was holding my hand. I couldn’t see her without lifting my head and shoulders, so I didn’t realize she was asleep - until she started the sudden twitches indicating dreaming. She would grasp my wrist tightly, then relax.
Eventually she awoke with a start.
I’d love to know what my wrist was in that dream.
My cat hears my garage door opening (which is two stories down) and uses that as a signal to come down and greet me at my front door. I know she doesn’t just hang out there all day, since she’s not there if I don’t use the garage door (but comes running once I do open my front door). And she gets agitated if I’m delayed for whatever reason, like doing something for 10 minutes in the garage before coming up.
My cat loves me because she is one moody out-of-control passionate being who will purr one minute, bite me the next, and at 3AM fish under the covers with her paws to bat at my toes because she is bored.
She is CRAZY!
…and I wouldn’t change a single thing about her…
My cat and dog cannot stand each other but they act like siblings. My dog was attacked by a larger dog and my cat rushed to his rescue. On another occasion my cat was in a fight with another cat and my dog came to her rescue. They also seem to express sympathy and understanding for one another when one is sick or injured. Other than that they fight like cats and dogs and appear to be mortal enemies.
Mine puts his arms round me and cuddles me, runs to greet me when I get home, and, um, pisses on things and attacks people if I go away for the weekend. It’s not even me who feeds him half the time.
Obviously it’s not human love, but it is cat love.
That’s not love. That’s an announcement that it’s FEEDING TIME and I’M STAAAAAAAARRRRVING.
Damn, I miss having cats (damn allergies).
Prowler definitely loves me, and I love her.
Let me count the ways:
She insists on falling asleep next to my pillow and holding my hand (as described by usedtobe above) every night. Squeezes my wrist to her chest/neck/head and tightens her grip if I try to remove my hand.
Gives me those kitty “eye hugs” - squeezes her eyes partway closed, very slowly. This is sometimes accompanied by a little pursed mouth kiss-looking thing. VERY cute. So, I reciprocate. This can go on for some time.
After I fall asleep she moves down to sleep lower on the bed, and she knows when I wake up. That’s her signal to make her way up to my head for kisses, head-butts and hugs. Sometimes she pats/pets my cheek.
I took a week long trip many years ago in my old house. I had set up with my brother in law to come feed them while I was gone. Well, he didn’t do it, and when I got home there was no food and no water. (They’d been left with a full bowl, so it wasn’t more than about 2 days with no food, still, I was a bit pissed about it.)
Anyway, Little Guy, my pride and joy, meets me. I pick him up. He bites me hard on the forehead, I yelp in pain, then he goes completely nuts licking my face and head.
Bite “I missed you, I’m mad!”
Licks: “But oh I’m happy to see you! I love you!”
My current cat Maggie will run up to the top of the cat pole, circle in the bed there and position herself head down but looking at me, tail in the air. This is so I can stand there rubbing and kissing her head while rubbing her butt with the other hand. It’s pretty obvious from the way she acts that this is all about love.
Okay, here’s one - if anyone has anything similar, I would appreciate hearing about it.
I have one cat that shows me he loves me by kneading my chin. He jumps on me when I am lying in bed reading, kneads my body, eventually plops down facing me, then reaches out with both paws and kneads either side of my chin. Yes, using his claws. Ouch but hilarious. He is purring like a motorboat the whole time, eyes closed, ears back with concentration.
About the only thing I can think of is that he is doing to me what he loves having done to him. He loves having his chin scratched, hard, and his face rubbed, too. He pushes his face into my hand. I think he thinks he is returning the favor. 
What say you, Doper cat lovers? Seen any cat do this? Have a better explanation than my hypothesis?
I think my cat loves me, but I also know that if my cat were large enough, it would happily kill and eat me.