I've only had two experiences with this sort of thing.
The first time I had to see a doctor for severe anxiety (though I didn't know it was that at the time). He was rude, contemptuous and basically acted like I was wasting his time. He even thought at one point I was making it all up! He referred me for a blood test and that was it. It wasn't until I confirmed I'd had terrible, bad thoughts that he knew mental illness was at work here and referred me to a psychiatrist.
The second time, more recently, I had another flare-up of anxiety and depression. I felt edgy talking to my doctor about this (a different doctor, mind) but he was extremely nice, listened carefully to what I was saying and even gave me a mini counselling session himself! He then offered me some more practical advice to combat my anxiety rather than throwing tablets at me, and told me to return if it didn't work.
I don't go to the doctors often about it because while my symptoms are kind of chronic, they're not adversely affecting my life, they're mild - plus I feel like I'd be wasting the GP's time anyway. But I agree when you say you get scared, because it is a frightening prospect discussing this sort of thing with them, for two reasons: 1) Depending on who you see, they might be quick to dismiss you or think you're a time-waster and 2) Mental health is a sensitive topic and difficult to open up about anyway.