There are a couple of well-regarded private organizations in the U.S. which write standards for and verify supplement manufacturers, one of which is United States Pharmacopeia (USP). See
https://en.wikipedia.org/wiki/United_States_Pharmacopeia They serve a similar function as UL does for electrical and fire safety; and like UL some their standards are incorporated into the regulations of the U.S. and other countries.
Only a handful of well-known supplement makers are USP verified, AFAICT. (Note, verified is different than simply claiming to adhere to USP standards. It's like the difference between FIPS compliant and FIPS certified.) I try to buy Nature Made, a common brand in pharmacies which will usually carry the USP Verified mark, though it's product specific (see http://www.naturemade.com/usp).
Like with UL, this doesn't mean you're not buying useless crap, but it means you're unlikely to buy crap that will kill you, which is adulterated, or which isn't manufactured to minimum standards of safety (e.g. lead content--many supplements contain surprising levels of lead[1]).
[1] Not surprising if you consider how ubiquitous lead is in industrial environments, and that using non-contaminated materials in your food processing chain requires comprehensive, sustained efforts which translate to $$, especially in an age when so much industrial equipment comes from overseas.
EDIT: Consumer Reports details four private verification programs for supplement makers, including a table of testing regimes: https://www.consumerreports.org/supplements/how-to-choose-su... To me USP looks the best--store bought samples, more regular testing, stricter criteria for ingredients. The other 3 players they discuss are NSF International, UL (branching out, I guess), and ConsumerLab.com.