When it comes to kneading bread dough, modern technology has given us a number of options. Of course you can use the old-fashioned hand-kneading method, which has the advantage of not requiring any special equipment. And it can be done just about anywhere you have a surface to work on.
One downside to hand kneading is that it can be hard on the hands and wrists, and it takes a bit of time. (Though some people find that hand kneading can be relaxing and calming—or, if you're using a more aggressive approach, it can relieve some frustrations.)
The "No-Knead Bread" trend has proved that dough doesn't need to be kneaded much—or at all—if you're giving it a sufficiently long rest. Gluten develops on its own in the presence of water, so kneading isn't necessary to develop the gluten.
But there's more to kneading than just the creation of gluten. The kneading process also "arranges" the gluten, for lack of a better term. The act of repeatedly folding and pressing and turning the dough creates a different sort of structure in that webby network. Whether that structure is better or not depends on the sort of bread you're looking for.
But what about machine kneading? Can a food processor or mixer replace kneading by hand? Using a machine to do your kneading changes the final product. While a food processor or a stand mixture does a fine job of developing the gluten in dough, neither one of them perfectly mimics the motion of hand-kneading. There are other differences as well.
A food processor kneads dough very quickly; in as little as a minute in some cases. It also heats the dough up while it processes, so if you need to knead longer, you risk heating the dough to a point where the yeast begins to die off. If your dough requires longer kneading, it's best to do so in short sessions with waiting time in between to let the dough cool off.
Since the dough coming out of the processor is warm, it also rises faster. This is a plus if you're in a hurry to get your bread made, but it's a disadvantage if you are hoping for a slow rise for more flavor development.
Since the food processor kneads so quickly, it's also possible to overknead the dough. When a dough is over-kneaded, the gluten breaks down and instead of a stretchy and elastic dough it becomes a puddle of goo that won't hold its shape.
Part of what happens during kneading is the incorporation of oxygen into the dough. Oxygen helps the gluten strands to connect to each other, creating the long strands that form the web of gluten that's so important.
But there can be too much of a good thing. Too much oxygen bleaches the dough, turning it whiter the longer it is kneaded. While that might sound appealing, the wheat pigment also carries flavor. As the dough oxidizes and lightens, it loses flavor. Because a food processor does the kneading so fast, there's much less time for oxidation to occur, and more flavor remains.
However, the action of the food processor is also the most violent, cutting some of the gluten strands as it kneads. You should also keep in mind that if you want large chunks of dried fruit or whole seeds in your bread or pizza crust, it's best to add them by hand after the dough is kneaded.
A stand mixer is somewhere in the middle of the spectrum between slow, soft hand kneading and the quick work of food processor. Since the stand mixer isn't as fast as a food processor, it allows the baker to watch the development of the dough and add ingredients along the way. It isn't as violent as the food processor and doesn't cut gluten strands. It's also less damaging to any additions you're making, so you can add seeds, nuts, and dried fruit and expect that most of them will remain intact.
While the stand mixer heats the dough a little bit, it doesn't get nearly as warm as a dough kneaded in a food processor, so you can knead for a much longer time without any fear of overheating the yeast.
It's also unlikely that you'll overknead a dough with a stand mixer. It's theoretically possible if you leave it kneading for a long period of time, but it's not going to happen in a fraction of a second when you go answer the phone.
While kneading dough with a stand mixer is slightly faster than hand kneading, some would say that cleaning the bowl and dough hook uses up any of the time you might have saved. This may be true, but I find another benefit to using the stand mixer: while the stand mixer is running, I can preheat the oven, prep the baking sheet or loaf pan, or do something else in the kitchen. I don't need to watch it as carefully as the food processor, and I don't need to interact with it constantly.
On the downside, I've heard the criticism that dough kneaded in a stand mixer is "too organized"—that the gluten strands are all following the spiral pattern of the dough hook rather than being more haphazard as in a hand-kneaded dough.
In the end, the kneading (or no-kneading) method you choose is a personal preference. And of course, you can mix and match the methods, letting a machine (or time) do most of the work, then finishing kneading by hand.