I've developed an understanding, that Russian and Ukrainian are somewhat similar like Spanish and Portuguese. I speak Portuguese and I'm able to understand more or less (quite well in fact) Spanish - thought I've never leaned it. But if you speak Spanish, it want be just as easy for you to understand Portuguese.
People who speak Ukrainian will rather understand Russian even if they've only heard it a couple of times in their life. On the contrary, if a Russian native speaker didn't hear Ukrainian before, he(she) will probably not understand a bigger part of the message made in Ukrainian (at least at first).
+ one interesting fact in addition: I once made an experiment with a girl from Poland which didn't know a word neither in Russian nor in Ukrainian before. she spoke Polish and I spoke Ukrainian, for an hour or so. we've just met so it wasn't because we knew each others mind well but we in deed understood every word we said/heard in the language which we never used before. And after that we tried to do the same with Polish and Russian - and she failed to understand the main (most important) part of each sentence..
So Ukrainian and Polish are closer in order to reach understanding - even though historically and linguistically Russian and Ukrainian belong to one language group while Polnish belongs to another.
Belorussian and Ukrainian are also quite close so that we can understand each other pretty well (like Polish and Ukrainian). And both these languages historically and linguistically belong to the same language group as Russian. But than again, Russian language speakers do not understand Belorussian as good as Belorussian language speakers understand Russian ;).