If you use normalize.css, that stylesheet will do something like input[type="search"] { -webkit-appearance: textfield; }.
This has a higher specificity than a single class selector like .foo, so be aware that you then can't do just .my-field { -webkit-appearance: none; }. If you have no better way to achieve the right specificity, this will help:
.my-field { -webkit-appearance: none !important; }