A (Jewish, Ashkenazi) friend recently asked, 'Should I have genetic testing for the Ashkenazi-Jew genetic syndromes?'
My advice to people, from a strictly practical level, is to consider the cost vs. the likelihood. If desired, one's personal making-me-crazy level may be added in.
Things like Tay-Sachs, while scary, tragic, and fatal, were actually quite rare even before genetic testing: 100 new cases per year in the entire country. The carrier rate is 1/27 for people of exclusively Ashkenazi (Eastern European) Jewish heritage; if two such people reproduce, there is a 1/1000 chance their child would have Tay-Sachs. (Laurie points out in the comments that two known carriers have a 25% chance, of course.)
The other recessive "Jewish" diseases occur even less frequently. The carrier rate for Canavan, for example, is somewhere near 1/100, so two Ashkenazi Jews have about a 1/10,000 risk for a child with Canavan.
In my particular case: my father is not Ashkenazi. Therefore my basal rate for Tay-Sachs carrier-ness is half: 1/54. The carrier rate in the general population is 1/200. My husband is also not Ashkenazi. Between the two of us, it's about 1/11,000. For contrast, in the general population, it would be 1/40,000.
In 1970, there were about 3.8 million births (and 100 cases) That's 1 Tay-Sachs case for 50,000 births. And? Nobody tests the general population for Tay-Sachs.
If 1/10,000 is an unacceptable risk to you- the testing is a good idea. In addition, many of the "Jewish" diseases are fatal, and most parents choose to terminate.
If one's risks of genetic diseases are elevated- family history, prior history in pregnancies, etc.- it might be a better idea to test. As there are a lot of things that can go wrong with genetics, however, there are many diseases for which there exists no test.
But bear in mind that all risk is relative. There are 21 yearly vehicle-accident fatalities per 100,000 drivers in this country. That's a 1/4700 yearly chance of dying in a car wreck.