Cowards are prone to pee self and pass out when they receive the "Terrified" moodlet, and they will always flee.[TS3:SN]
When directing a coward Sim to try and attempt to cross a booby-trap, they won't do it.
Coward Sims will react badly to the "Tell Ghost Story" interaction.
Cowardly Sims cannot apprehend a burglar, even if they have the Can Apprehend Burglar hidden trait from working in Law Enforcement or inheriting the hidden trait from their parents. The option to fight will appear, but the Coward will run away and/or faint at the sight of the burglar.
Cowardly Sims are at a disadvantage when undertaking a Technology major while studying at college.[TS3:UL]