Electronic devices may have sensitive circuitry. To determine whether an electronic device has been exposed to excessive amounts of moisture, the electronic device may be provided with a moisture indicator. The moisture indicator may have a wicking layer of white paper and a red dye layer. If a portion of the moisture indicator is exposed to moisture, red dye may bleed into the white paper. The moisture indicator may be mounted in an input-output port opening or other portion of the electronic device where the state of the moisture indicator is visible. The moisture indicator may have sealed edges to reduce sensitivity to small amounts of moisture intrusion. Different regions of the moisture indicator may be provided with different sensitivities by forming structures that have altered moisture flow properties, by altering wicking layer thicknesses, or by otherwise spatially modifying moisture sensitivity.