How large can an apparent size of a moon be?

In a lot of media one can see moons or other planets that cover a significant portion of the sky (like the background on this page for example). This could be because the moon is actually large or because it's close. Presumably, though, if a moon is too close or too large it will cause catastrophic gravity related destruction.

I'm wondering if it would be possible to have a planet that's more or less exactly like Earth, whose moon would appear to be much larger in the sky? Can it be, say 90 angular minutes without coming within Roche limit or causing deadly tidal effects?

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How large can an apparent size of a moon be?

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