If you have multiple cats, I guess just answer in the poll for whichever has the most pronounced preference, and post about the other cats in-thread.
We have two cats. It’s a common occurrence when we’re leaving the living room that they’ll both join you and try to lead you in the desired direction: Xena will try to lead you to the kitchen, where the food is, while Gabby will try to lead you to the bathroom, where the brushes are. Xena would weigh 50 lb. if we gave here as much food as she wanted. Gabby, I’m convinced, would starve to death if we only ever offered her the choice of being fed or being brushed. She’s basically an addict, but I can’t make any other living thing as happy as I can make her with two minutes of brushing, so I indulge her more than I should.
So, what do your cats live for?
Hunting, closely followed by being petted.
We live in a rural area and Mitzy’s current record is seven rodents in one day. She doesn’t play much, but I assume that’s because her play needs are being met by her hunting. She’s always extremely vocal when she brings home a kill, and will carry it around the house to show other family members if the first person doesn’t seem impressed enough.
In the evenings though, her favourite place is in my lap, being petted.
Being held.
My oldest cat isn’t happy unless he’s being held. Sitting in my lap isn’t enough.
All of our cats are barn cats. I don’t think I could get close enough to any of them to pick them up. They are there to keep the mice and rodent population down.
My cat loves to play fetch. She’ll have me throw a hairband, chase it down at full speed crashing into anything in her way, and bring it back to me to throw again over and over until my shoulder falls off. If I stop she just sits there whacking me with her paw until I throw it again.
Trying to reach the ceiling.
He looks up at it and yowls several times a day. He attempts to get up there via the blinds, a wall tapestry, from the bed or by launching himself from whatever perch he can find. There’s nothing up there, so I chose “playing” rather than hunting.
Dehydrated chicken treats and sleeping on anything warm: my wife, me, heating pad, laundry fresh out of the dryer, laptop vent…
I went for being brushed/petted, though it’s more than that. All three of them live for being cuddled and picked up and carried around. 
My two love sitting in my lap. I had knee replacement surgery at the end of April and they haven’t been allowed on the lap since. I guess it’s about time to let them up again but what worries me is they’re both fairly skittish and if the phone or the doorbell rings they tend to launch themselves off me. I don’t think my incision and sore muscles are quite ready to be a launch pad. In the mean time I have persuaded the boy kitty to sit next to me in my chair and be petted, but the girl is indignant that I would even think that was some kind of substitute.
All this is not to say that they don’t love eating; they do. But they love my lap more. (Insert smug smile here.)
Oh yes: picture here; boy is yellow.
Pooping. How could this not be on the list?
One lives for food. Anything that could ever be considered food by anyone. This includes pathetically staring at us while eating paper, just to show that his life is SO SAD HE’S EATING PAPER.
The other lives for attention. And pouncing on buttons on your shirt. Preferably while getting petted.
Ours lives for the cat TV to be turned on every morning. You probably think of it as “opening the blinds and the window”, but to her it’s a sensory delight akin to a human binge-watching a favorite series.
My cat (well, the one with the strongest preference) lives for the red dot. He’s obsessed with hit. He will have it. I picked “hunting” as the closest fit.
One of my other cats lives for having a warm butt. If his butt is warm, he’s happy.
Dried anchovies. I don’t think my cats ever imagined something so delicious existed in the world. If youtube existed when I had my cats, I could have made billions because they would do anything for those anchovies. I taught one to fetch, sit, lie down, shake hands, and roll over just because of anchovies. The other one could be hypnotized using anchovies on a string. Both of them would stare at you with horror, disgust, and/or disdain if their food bowl only contained kibble.
Going in and out. Damned cat.
Go to the cats, observe their ways, and be wise.
My sister has cats, and they seem to live to fight with each other.
One of 'em is one hell of a killer, and brings back dead birds, gophers, rabbits, and the like.
They also seem to live to wake people up at five a.m.
There is something on my nightstand he longs to eat, kill, or fuck. Possibly the nightstand itself.
Three cats. Main diversion: jockeying for position in our bed after we have retired for the night. Usual result: “GET OUT!” Then they return after what they regard as a decent interval.