I didn't tell them until I was in my mid-twenties, even though I'd known I was into women for a decade. I'm not sure why: I was pretty confident that they wouldn't care because I had a gay uncle and they had never treated that like it was an issue. I think it was just because I hadn't had a significant relationship with a woman until that point; I'd dated around but never introduced a lady to my parents, and my previous relationship had been with a guy (it didn't go very well).
Anyway, I was visiting one night and kind of blurted it out over dinner. The first question my mom asked me was "Do you have a girlfriend?" and I told her that I was very much single at the moment. My dad told me that if I do meet someone important to me, they'd love to meet her, then poured me another glass of wine.
The next day my mom asked me a few questions: how long had I known, why hadn't I told them before, what about [ex-boyfriend], etc. I asked her if they had known beforehand, and she said they had thought I might be, something about my hair/clothes/hero-worship of strong female figures. She reiterated that if I wanted to introduce them to the next person I dated they would love to meet her. She said "You know we love you no matter what, right?". It was nice.
I guess the only thing they did that I didn't like was not tell my extended family for quite some time. I don't really see them more than once a year, if that, but my parents do. So I didn't really care about telling them myself. They didn't keep it a secret, exactly, but it took them a while to tell my aunts, uncles, and cousins. I think they were waiting until I started dating someone, because when I did they told the rest of my family pretty quickly.
They've been really supportive throughout. They love my girlfriend and call her their daughter-in-law (we're not married). The other day my dad asked me if I think he should watch Orange is the New Black. I definitely got lucky.