Most things are affected a bit, worst of all, galaxies. But brighter open clusters and globulars can be surprisingly rewarding, especially if they're in a part of the sky away from the Moon, and the moon is no more than a mid-gibbous phase (70% or so), obviously ideally if the Moon is a bit lower in the sky too. If you have a nebula filter you can see lots of detail in the nebulae of the Magellanic Clouds, Eta Car, M42 etc, if transparency is decent, often not a huge amount less than without the Moon! Planetaries will also pop out with the filter even under moderate moonlight. If you're into them, hunt down a few double stars, they're basically unaffected, and can be quite rewarding if you go out with a specific aim of seeing a few. Bright planets of course are fine too. Obviously depends on your equipment, but if you scale your expectations and targets right, you can be surprised at what you can see.
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