I came up with six other current statewide elected officials whose fathers were governor (see the list below). If I'd counted appointed officials or those who don't hold statewide offices, my list would have been much bigger, including folks such as state Senator Chris Romer in Colorado or state Senator Thomas Kean, Jr. in New Jersey.
Of these six people, all of them, like Cuomo, are Democrats. The most likely explanation for this partisan slant is coincidence. The second most likely explanation is that there are lots of other sons and daughters of governors who I didn't discover (I'd love to hear additions to my list).
However, here's a theory in the event that those two explanations are wrong. Between the Republican Revolution of 1994 and the 2006 Democratic revival, and especially in the 2002-2004 timeframe, the Democratic Party's image was generally poor. In that context, Democratic Party leaders eagerly recruited "legacy" candidates, whose golden names could overcome their leaden party label.
That said, the evidence I have here only partially supports this theory. It's not as though New York Democrats were in despair in 2006, which made them seek another Cuomo. Regardless, it will be interesting to see whether Republicans start recruiting famous children in time for 2008.
