In regular low voltage multiple-pin circuit connectors, such as automotive applications, flooding with a proper insulating grease of low-viscosity dielectric grease is perfectly acceptable unless a manufacturer recommends against it. The grease should have good stability and not contain metals in any form, and be specifically designed for use as a dielectric grease. This generally is a silicone dielectric grease, although some Teflon based greases are acceptable.
In single low-voltage terminals or connections, such as metal-to-metal joints, grounds, or battery posts, almost any pure grease of light viscosity will be acceptable. Caution should be used with greases containing metallic powders to be sure any metal is compatible with the embedded grease metal. Connection enhancement from embedded metal powder is very minor, if it exists at all, and there is increased risk of bad connections if the metal powder has any interaction with the base metals.