I avoid meat (not vegetarian, just eat as little as I conveniently can) because of what I and my friends call the Stuffed-Animal-Principle. The idea is that it's bad utility function maintenance to allow stuffed animals to be abused. (Stanford burned teddy bears in the pre big game rally.) The idea is that stuffed animals are basically a technological superstimulus for empathy and you risk damage to your actual utility function by desensitizing yourself to that. (I don't have actual studies on the specific fact, but it makes sense with things that are known.)
Actual animal suffering is far more upsetting to actually witness. Mostly our society avoids this problem by putting it out of mind and just enjoying the results. We also do this for many problems that affect humans allowing them to continue and I really don't want to train my own ability and willingness to ignore suffering I'm complicit in just because it happens to not actually matter as much as it looks.
I have various friends who do meat limitation for this reason; one is even a full vegetarian. I have no idea how common it is though.
Hiding animal suffering probably makes us "more ethical". Vegetarians are usually people who were raised in cities. People who grew up slaughtering animals often can't even comprehend that someone else can have a problem with it.
I notice that a large fraction of Effective Altruism people are vegetarian. This makes sense: in general Effective Altruists take moral issues seriously, even when that means changing your lifestyle. I'm not sure it's a good balance, though.
One way to think about this is to convert it into money. How much would I need to be paid to give up eating meat? All animal products? How much money would I need to spend on myself to be about as happy as I would be with less money but continuing to eat animals? I'd probably be willing to go vegetarian for about $500/year, vegan for maybe $2000/year.
It turns out you can probably pay to convince other people to be vegetarian much more cheaply than that. I estimate the cost of a vegetarian-year at $4.29 to $536 while Brian Tomasik estimates $11 with better methodology (which I looked at). This is by placing ads on facebook for a site where people can watch an animial cruelty video and ideally become vegetarian or vegan.
If you would get more than $11/year worth of enjoyment out of continuing to eat meat, why not give $11/year to convince someone else to not eat meat for you? Or give $50/year and be on the safe side?
(While you're giving money, you should probably give it to the organization that you think will do the most good with it, which I think is probably one of GiveWell's top charities. The nice thing about money as opposed to actions is that it's easy to redirect.)
I also posted this on my blog.