Are tickets to previews of NYC plays available to the general public? Is there any chance of finding them at TKTS? Next weekend my son and I hoping to see either Metamorphoses, The Goat or The Crucible.

Yes, many times TKTS carries preview tickets, especially if the show is not going to be a sell out (such as Mama Mia or The Producers). I'm sure you can get tickets for the shows you've listed off TKTS.

However, check the following website. They list daily (after 4 pm) what is going to be on the TKTS boards. If you look at it for a few days, you can see what patterns develop.

http://newyork.citysearch.com/feature/34843/

What I meant above is that Mama Mia & Producers were sell outs and therefore would never appear on TKTS. Sorry for the confusion.

To answer the first part of your question, yes, preview tickets are available to the general public the same as "regular" (i.e., after the critics have reviewed the show) performances.
Chances for finding The Crucicle at TKTS are possible, but probably less likely than the other two.

I saw The Goat in its second day of previews, and I got the tix at a discount via a code in an ad in the New Yorker magazine. I don't remember the date of the issue, but I'd guess it was the one from 3 weeks ago, with a skiier on the cover.