Personally, I say no to guys who ask me out if we're not friends. Doesn't mean you can't ask out, then be friends though (provided you want to actually be friends).
My fiancé for instance asked me out, I said no because I didn't know him well enough. Then we became friends and after a few months I fell in love with him from being friends (and in big part because he never asked again. Very disrespectful to be pushy). So I asked him if he was still interested in dating, and he was.
Of course I risk people losing interest in me, but if they lose interest when we become friends, I figure we weren't compatible in the first place.
The thing to understand about the "friend zone" is that there isn't a zone you enter the second you are friends that makes you undatable. The way it works isn't "you're in the friend zone so she won't be interested in you". It's "she isn't interested in you, SO you're gonna stay in the friend zone".
In other words, if I hadn't been interested in my fiancé, we'd still be friends. And he might feel like he's in the "friend zone" and it's "too late". But the reality is, when you're friends with someone, they get to know you. So if they don't ask you out or are interested, when they know you so well, they won't be interested in you. Period.
On the other hand, some people don't date people they don't know well. As I said, I'd never say yes to someone who isn't a friend. I need to trust someone enough to be willing to date them. I'm not a rarity, I've asked around and most of my girlfriends prefer it to be that way. Sometimes they meet someone, talk and hit it off and are willing to go from there, but there is a big unknown and the guy could turn out to be a jerk, etc. Getting to know each other first feels more safe.
Anyway, as I said, asking first isn't necessarily a bad idea. You can throw it out there that you're interested. Then she says yes or no, and if she says no, you can still be friends and she'll know you're interested. The problem is, then you can't really ask again without running the risk of being pushy. So only do that if you want to at least be friends, and not just to get the girl, because she might very well never be interested.
Same thing if you become friends without asking. And I'm going to let you in on a secret. When a girl says "I don't want to ruin our friendship", she doesn't mean "you're in the friend zone now. I'd love to date you but I just can't". 99% of the time, what she means is "I'm not interested in you at all, but I'm afraid I'll hurt your feelings if I say so. Plus you're a great friend and I don't want to lose you". Because if she does feel the same, believe me, in my experience, she will say yes or even ask you out/seduce you first.
In a small portion of the cases, it's possible that the girl is genuinely worried she might ruin everything forever if she dates you. That's usually the case when she lacks self-confidence. I'm not sure what you could do as there isn't much of a way to identify that 1%, so you might still have to bite the bullet, be just friends, and see if she ever gets more self confidence, but not wait for her.
So, that's pretty much it... Good luck.
And to answer your question, yeah, all my relationships have started with friendships and I wouldn't have it any other way. On the other hand, being my friend doesn't mean I'll date you, either. I wouldn't date most of my male friends. That's why I didn't ask them out when I was single, because I like them, they're great friends, but we have no chemistry and I don't see myself sharing my life with them. They're not in the Friend Zone, they're in the "we're not compatible" zone and they're my friend. That's not the same thing from my point of view.
