Lifelong sufferer of impostor syndrome here (after having failed university), now Cofounder & CTO of a pretty successful Series B startup:
1. Work together with awesome people who can reflect you. Now that I'm working together with world class founders that I fully trust and we're doing regular feedback sessions with each other, I can take confirmation of my abilities much more serious from them than from anyone else.
2. Practice self-love and compassion. No, really. I'm serious, there's a ton of studies about this. Get a therapist. Best thing I've ever done for myself.
3. If you compare yourself all the time with others, that's okay - but do so fairly. People like us love choosing the best ones worldwide for comparison and that does nothing but inflict useless pain. Instead, take the next 10 of [insert your job title here] that you can think of and compare yourself with them. If you compare favorably with at least half, you're average already (which means you're not an impostor).
4. Keep this diagram in mind: https://twitter.com/rundavidrun/status/587671657193455616
Big part of impostor syndrome is devaluing the stuff you already know (but others don't) since it's "common knowledge". If someone else appears to know more than you, they're probably just as smart as you are. If they know as much as you do, they're certainly less able.
5. Fake it 'till you make it. Citing http://www.defmacro.org/2014/10/03/engman.html here: "Believe in yourself. You can’t lead a cavalry charge if you think you look funny on a horse."
6. Ask yourself better questions. Tony Robbins once quipped: "Your brain is a computer and it will try to answer any question you give it. You may not like the answer though." So instead of asking yourself
7. Success definitely helps, but it doesn't cure. It's also the hardest to come by as there's some luck, good timing and great people involved along the way, so work mostly on the other things instead.
8. If you still think you're an impostor, rest assured you're in good company. We impostors are pretty smart people. Frank Abignale passed his bar exam without cheating and Ferdinand Waldo Demara successfully operated on people as an untrained surgeon. :)
I think by now I'm 50% done with that topic, and as `hajak` wonderfully put it - don't worry too much about it, it's not just a curse, there's good sides about it too.
EDIT: Slightly amended the list and copyediting