I can't talk for everyone else, but concerning me, even if a call ten vets, they will usually all tell me that they have to see the animal in question. Half of the time I went for nothing, wich is upsetting because of my money problems (as someone else said, though, I think my cats are better with me than in a shelter even if I couldn't afford a 1000$ visit for now). I wouldn't spend money on other things and when I'll be able to save some money, I will first do it for them.
So, in my case, when something is far from being an emergency but still bothers me a little, I'll make some research on the net, ask a few questions in forums and call a vet. With all these different sources of advice, I can sometimes take care myself of my pets!
My other point is that some little problems appears at night or during week-ends. I don't know, but I'm afraid of calling an emergency vet because my cat coughed three times in a day! By getting information on "is it the first signs of something that could endanger the health of my cat in the future?" here I feel that I'm actually doing something to help my cat until I call the vet.
My last point, people are anxious when their pets are sicks and they might be seeking for support. Even though I call the vet and see her with my sick babies, I'm more than happy when people here are also trying to help me. I found interresting tips on how to introduce a new cat in my home, on pregnancy and delivering, on kittens, on how to help a cat heal a cold only by starting one thread where I was worried about my Maya sneezing.
Finally, even if there are goods reasons to ask a health question here, a pet owner should always go to the vet during the next 24 hours four a little problem that didn't go away. I've learned how important it is to save money for our animals too. I lost Maya in less than three days: she stopped eating, I waited 48 hours instead of 24 before going to the vet because I was hoping she would start eating again. When I went there she needed to be hospitalized (1000$) and I couldn't afford it. I took her back home and she died less than a day after even with all my efforts to keep her alive, even with all the medical advice the vet had given me, even with all the support and tips I got on this forum.
Why? Because I couldn't afford to keep her alive, because I waited to long before going to the vet. Please, never make the same mistake as me. Go to the vet as soon as you find something unusual about your cat/dog/pet. This could save their life.