What's the closest Venus gets to the moon? I recently observed the beautiful sight of Venus quite close to the crescent moon, and was wondering, what the closest (angular distance as seen from earth) they come.

Are there on-line tables or calculators for finding when such nearest events occur and are visible?
Venus is, on occasion, occulted by the Moon (that is to say, the Moon passes in front of Venus as seen from our point of view).  Exactly when that happens is dependent on your location on the Earth, since the location of the Moon in the skies varies by about a degree or so depending on your location on the Earth, and of course, it might be on the other side of the Earth when it happens (it only lasts about an hour or less).  From North America, it happened in December 2015; it will happen again in September 2017, but only from Australia and neighboring countries.

If you google "Venus occultation" you should get something like what you want.  ETA: Here's one link: http://www.lunar-occultations.com/iota/planets/planets.htm