I do a tremendous amount of culling... My criteria varies all over the place, but I'll give some examples...
Watermelon: Some years ago, we gathered together hundreds of varieties of watermelon, and let them cross pollinate. We included some wild watermelons in the mix.... So we picked up two undesirable traits. First was that some of the seeds were "hard". That means they didn't absorb water and germinate with the rest of the crops. Culling for that trait was as easy as going through the patch about a month later, and culling any plants that had just germinated. "As easy as..." Sheesh. There are so many things going on in a garden, it's not always easy to catch things at the right time to cull. But eventually I mostly got it right a couple years in a row, and the hard-seed trait went away. The other wild trait we picked up from the wild melons was "exploding melons". Basically, the rind was so thin that the melons would get ripe and burst before we could pick them. Eliminating that trait meant not saving seeds from any melon that had exploded. It was harder to eliminate than the hard-seed trait, because by the time a melon is exploding, it has already shed it's pollen into the patch.
Muskmelons: The first few years I grew muskmelons, the most important trait was survival-of-the-fittest. They had to make seeds in my garden. Then that changed to earliness of fruiting. These days I cull a few slow growing plants, but the highest priority selection factor these days is amazing taste.
Corn: Vigorous growth of corn plants seems critical in my short season. It seems important to get the cobs high
enough off the ground to prevent predation by mammals and birds. So I often go through the patch and cull corn plants that are growing much more slowly than the rest.
Here's an example of culling based only on the size of the plants. I don't remember if I took both of the slow growing plants or if I left the stronger of the two.
This corn plant was culled for what I thought of as a genetic defect. It lacked sufficient chlorophyll in it's leaves. There were a number of plants from the same parent with the same trait.
Squash: There might be times, when I don't cull a plant, even if it is growing slowly, especially if it has a trait that I'd like to explore... For example this squash has leaves like I have never seen before among it's species, or any squash species... I wonder if it's an inter-species hybrid? I liked this plant so much, that I culled the robustly growing, healthy plants next to it, to give it plenty of space to grow and develop. Especially in squash, I pay a lot of attention to keeping plants that are different than their peers. I value different leaf shapes/colors, and different colors/shapes of fruits, and different types of vines. All things being equal, I tend to keep the things in my squash that are different from their peers, even if it means I am selecting slightly less productive plants. I found one moschata squash plant this year that looks like the mother might have been pollinated by Curcurbita palmata last growing season. It's a keeper. Photo to follow. I didn't cull another squash plant with very odd leaves. It is growing very slowly. It's well on it's way to self-eliminating.
Odd type of squash. Definitely keep this one since it might be an inter-species hybrid.
Beans: I don't do much culling on beans. I figure that those that succumb to disease, or to lodging are mostly self-eliminating anyway. And those that produce the most seeds are well on their way to dominating the population. That could be detrimental, if I were selecting for plants that produce lots of small seeds instead of fewer/larger seeds. Not that small seeded beans are undesirable... It's just a choice: People like their large beans, even if it means that they get less total yield. I cull the bean patch to keep the plants mostly growing as bush beans instead of pole beans, but other than that, I tend to leave them alone.
For the first few years after I start developing a new
landrace, I tend to keep culling to a minimum. I am mostly interested in survival-of-the-fittest culling. Let whatever can produce a seed here go ahead and do it, and hopefully it will cross pollinate as much as possible with other plants that might be able to produce pollen here, even if they can't produce a seed. Then after a few years, I start selecting more heavily for production. Then once I get a variety that does really well here, I might not cull much any more...