According to the maths done on the XKCD "What if?" feature, if you were close enough to a supernova, even if you could dodge all other forms of lethal radiation you would be killed by neutrino exposure alone - which is a ridiculous concept given how billions of them pass through every square centimetre of your body's surface area every second without any effect:
http://what-if.xkcd.com/73/
But our ships have extra sturdy hulls and mega powerful shields to protect us against those pesky tiny particles travelling with ridiculous energies.