The topic of mutual intelligibility in Slavic languages is a bit difficult. For example, Bulgarian is routinely regarded as a language most distant from the Slavic type and very difficult to understand for most Slavs. In Czech, there even exists a saying "speaking like a Bulgarian" for unintelligible speech. Yet the difficulties in understanding lie mainly in grammar (the non-existence of word-endings, the use of articles). You can listen to a Bulgarian, not to understand a word and doubt, if you are actually listening to an Indo-European language - and then you see a Bulgarian text and you are surprised that you can read it quite with ease. So the difference in understanding spoken language and written language can be huge. 
As for the difference between Czech/Slovak and Polish, I must agree with the Polish contributor above that a fluent conversation is not possible. Yet you can certainly understand a lot and conduct some conversation, if you try to be patient. So "a limited intelligibility" would be a more correct term. As for written Polish, Czechs and Slovaks shouldn't have any difficulties with a general understanding Polish text, although quite a few words (especially of technical sort) may seem obscure and untintelligible. However, the closest Slavic language to Czech (after Slovak) is Lusitan Sorbian, especially Upper Sorbian. I don't have any personal experience with this language, but from the written texts I saw I think that its resemblance to Czech can be compared to East Slovakian dialects (which means that you can understand some passages easily, but subsequently you can be lost due to accumulation of weirdly sounding words.)