The first two years that we lived in our new builder-painted house I continually repainted the bottom 3 feet of the walls with the touch-up paint kit they gave us at the closing. Touching up was really the only option because trying to clean the wall would result in paint (or worse, texture) coming off the walls. Finally, I picked a new paint and started to repaint everything. I have now repainted, like, 10,000 sf of painted surface in the house, and then, let my little mess machines go crazy on it. It's given me a pretty good idea of what works and what doesn't.
1) Use a paint brush and a roller. This, it turns out, was the problem with the original walls. Sprayed-on paint is inherently inferior. The problem with spraying paint is an additive, or thinner, needs to be added for the paint to go through the sprayer. The thinned paint covers evenly, but predictably, THINNER than a brushed-on, rolled-on paint. Thin paint is more likely to chip, flake, or be washed off. Spraying is standard in the construction industry, so this tip might be the same thing as saying it's better to DIY than hire out when it comes to wall paint.
2) Avoid 1 coat coverage paints. It's tempting, because one coat paints generally give a nice, even coverage for very little time! You also feel like you're saving money because you only need one can of paint instead of two! But kids just look at the stuff and it falls off the walls. Don't do it; unless you're a conscientious adult living a quiet, peaceful and solitary lifestyle.
3) Choose non-texturized wall surfaces. Well, almost nobody has this option when choosing a place to live. But if you could have an option, this would be the one to take. There are simply less "edges" to hold dirt on a smooth wall finish. There is one ray of hope if you are stuck with texture walls, like most of us: you minimize the severity of the "edges" if you paint texturized walls. A layer of paint can smooth out the deeper crevices and be one less place for the dirt to wedge itself.
Aside: The majority of homes in the US come with some sort of texture on the wall surface. The type of texture seems to vary regionally and also based on when the house was built. You can see ours in the photo above. Home builders texturize walls because it's less expensive than making the wall smooth. Generally, the smoother the wall is, the more layers of joint compound have been added and sanded and added and sanded on top of the drywall. Texture, by contrast, requires no sanding and can disguise poorly installed drywall (where, perhaps, an drywall installer failed to drive a screw into a stud). At this time, there's also not a lot of demand for smooth walls in the United States, so there aren't as many contractors with the expertise and motivation to make walls smooth. It's sort of vicious cycle that someone would have to put financial muscle into breaking: I asked our basement contractor about smooth walls for our basement remodel and it was going to cost about $2K more.
4) The finish of the paint doesn't matter (as much as how the paint is applied). In the early days, I had a lot of people telling me that the problem with the original builder paint is that is was flat, as opposed to eggshell or satin or semi-gloss. I'm actually happy to report that this is not true. You don't have to have shiny walls for them to be durable. You just need to have a good coverage. (See numbers 1 and 5.) This became especially apparent over the last few years as various foods and drinks have exploded onto our ceiling. It was a flat finish paint, but, being newly repainted by me, it had good coverage. The food stuff wiped off easily, even when it once went unnoticed for about 24 hour. (How I could NOT notice pink EmergenC spray all over the ceiling for 24 hours, I still don't know....wish I had a photo of it!)
5) Paint smaller portions for better coverage. When using a roller, I generally try to limit myself to covering about 4-6 sf (an area of about 2 feet x 2-3 feet) before dipping back into the tray for more paint. It's difficult to find the right balance between a roller or brush that's dripping paint everywhere and a coat of paint that's too thin. I tended to err on the side of a too-thin coat since I'm easily annoyed by drips. Once I came to the conclusion that I just needed to paint less area and go back for more paint more often, I mastered the perfect coverage. I also never expect to paint a new color on a wall with less than 2 coats.
Aside: I think I was deluded by thinking I could cover an area of about 9 sf after each dip of the roller. Once upon a time, paint cans instructed with this really lousy diagram of a roller painting a "W" on the wall. Being naturally sensitive to scale and proportion, I sized up the diagram in my head and tried to paint way too much wall for years. How much you can paint is going to vary based on whether or not the walls are texturized. But generally, less is more. Also, make that a very tight and narrow "W" if you are going to use it (and I'm not convinced you must).
If you've made it this far, and have other tips, I'd love to hear them! I'd be especially curious to hear about various brands of paint. I've experimented quite a bit other Behr brand paint, because I live so close to Home Depot that it just keeps my life easy, but I know from working in architecture offices we always specified Benjamin Moore.