I've also got a stutter. Been aware of it since I was 11, and done a couple of weeks in speech therapy around that time where I learned some tricks like slowing down my speech, which has helped a lot over the years, especially as I have a tendency to speak fast.
Growing up, I used to be absolutely terrified of answering the phone, though fortunately, not so much anymore. I've been a remote employee for the past couple of years though, with most of my interaction with co-workers being via phone/email/IM, and there have been some moments when my words have got completely stuck on morning stand-up calls or conference calls, which isn't a pleasant feeling.
Equally terrifying was having to read out loud in class, which used to make me break out in cold sweat, or having to introduce myself to people. Strangely enough, I really enjoy reading to my kids nowadays and don't seem to stutter much when doing so.
I've noticed that it usually comes out more when I'm tired or stressed, and on those days, I try and stick to IM or email as much as possible to try and help with communicating, rather than stumbling my way through phone calls.
Being from the UK, but living in the US for 11 years now, one of the things that has helped is being forced to slow down my speech anyway as some people and co-workers struggle with a strong British accent.
I'm more of a covert stutterer though, instead of overt, and I'd guess that many of my colleagues don't even know the mental gymnastics involved to keep it that way, using things like slow speech and word substitution.
One of the things that does still completely suck is social interactions and coming across as awkward, because I always need to think about what I'm going to say, instead of being able to rapidly speak and respond in free-flowing conversation. I don't think that's something that will ever change.
Not sure if it's genetic as I've got a few family members who also stutter, though one of my worries has been that my kids will inherit this gene from me. Fortunately, my daughter seems to be a little chatterbox, though my son isn't talking yet, so only time will tell.