There were some experiments done in microgravity in longer space shuttle missions. The reports show that the fungi develop relatively normal but grow in random orientations instead of orientating upwards. See this images:
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The upper image shows fungi grown on earth which are subjected to normal gravity. The lower image shows fungi (actually only the fruiting bodies) which are grown during 7 day on the Spacelab D2 mission. The fungi obviously have a way of detecting gravity to let their fruiting body grow upwards. The image is from here, the article contains more information about this. There is also a publication in this topic:
* Mushrooms in microgravity - Mycology at the final frontier