I haven't managed to "convert" anyone to veganism, but I have at least helped to dispell stereotypes and spread awareness. Most people's experience with vegans is just the extremely vocal and perhaps extremist ones you find online, calling everyone rapists and murderers. And look, I understand that there is some logic behind that, but if your goal is to try to bring more people towards veganism, you won't do it by insulting people.
I've managed to convince most people that vegan food isn't gross. I offer people little bits of vegan food that I make or eat and they're often impressed.
I've dispelled myths about imitation meat being really unhealthy (not arguing it's healthy, but some people act like it's the worst thing you can eat). You'd be surprised how many people think it's some lab made nasty chemical.
I've dispelled a lot of myths (always respectfully, of course) about vegan nutrition. Most people aren't trying to be harmful, but they've heard a line or two online about how vegans can't build protein, can't get certain vitamins, etc.
Mostly, I think by just being a respectful and amicable human being, I've shown people that you can be vegan and not make your whole life about it. Most people don't even know I'm vegan until we eat together and I have to explain it. I don't want veganism to be some kind of religion or cult you have to join, I want it to just be a normal thing that people choose to do for the animals.
That being said, I do hope that I can eventually convince at least one person to become vegan, but I think trying too hard will just have the opposite effect. I'll continue to live by example and hoping people follow.