These detergents lather well (which surveys show people like). The most common types are sodium lauryl sulfate, ammonium lauryl sulfate, sodium laureth sulfate and ammonium laureth sulfate. Note laureth versus lauryl. The -eth suffix means oxygen has been added, making it milder and more watersoluble. Laureth sulfates may not cleanse as well but won’t strip as much oil—some people find lauryl sulfates too drying. (It’s a myth, though, that they strip colour. Even water alone speeds fading.)
Sulfates also bind to skin, so they are harder to rinse and may leave a residue that can cause irritation for those with sensitive scalps. (If this is you, try a laureth sulfate or sulfate-free formula.)
Bottom line: Sulfates aren’t an issue for most, and if you use styling products or have oily strands, you might prefer their clarifying effect.