Catster recently posted an article Do You Judge People Who Give Away Their Cats? by Eden Strong. This is my experience.
When Samantha was our cat in the early 1980s, we let her have kittens once. We kept one of her kittens (Sandy), gave one to my father's sitster, and gave the other two to the same people. I did get to see Bernie (né Brillo) when we visited my aunt.
When my parents moved to a farm in Missouri, the people who had previously lived in that house left behind two intact queens. They decided having feral cats was better than having mice or rats, so they fed them, but kept them outside (we were not sure how long they had been outside, for one thing). The dogs soon decided the cats should eat in the shed. The shed also gave them a place out of the wind and rain, and a place where we could put a litter box.
However, most of the cats were allowed to remain intact. We tried taking the kittens to the grocery store. They let us sit outside and give them away. At first, I was sad because I was losing my kitten friends. Later, I was sad when they did not find new homes and had to come back with us. Nospot (he looked like his sister, except she had a white spot on her back and he did not) ran away from the grocery store.
The following spring, four queens had litters within about a month. The first three queens thought there were too many kittens. I decided to keep one or two and take them with me. We tried to give others away, and were resonably successful. Some (including Schwarzie and Stripe) went to other farms; some may have gone inside (Mr. Gray and Miss Gray). One lady came up and said she couldn't take them now, but in a couple of months she could; she did contact us and take two of them (Little Blackie and Kiwi).
The two I wanted to keep, and two others we just could not give away at the time, were TNR'ed; they only had four places and two spays available on the day with the next available cat surgery. They hung around for a while. One of my two favorites (Butler) died the following spring. Truffles disappeared while I was making final plans to leave the farm. Inky did not want to go inside when I offered to put her inside one time, so Parker came all on her own.
In the fall just before Inky, Truffles, Butler, and Parker were fixed, we took Sir Ed to a family we knew from church. I was a little sad that he would be staying outside, but he did appear to like it there when I visited to see their kittens when I was deciding whether or not to take Parker.
There were other cats, such as Friendly and Beardy Cat, who disappeared; some others (Old Mr. Grey and Mama Kitty), were found dead. There was another who had to be put down.
I guess it all comes down to this : You love your cat; do you want her with you, or do you want what's best for her ? (or him)
UPDATE: Since it has been a common theme in the comments, I'd like to address the free giveaways. I did try contacting area rescues I found on Petfinder for the kittens of Sir Ed's generation. Many said they were full; one said they were full and there's a $30 surrender fee. I was able to find a rescue that would take Champ, Blair, and Graham ; Graham found his forever family almost immediately.