Adopt-a-Cat Month®. From the American Humane Association.

Adopt-a-Shelter-Cat Month. From the ASPCA.

National Pet Preparedness Month. This month, timed for the first month of hurricane season, urges people with pets to make preparations in case they should be hit by a disaster…and that includes making plans for what you would do with your cat in case of a hurricane, tornado, flood or other natural disaster.

June 4: Hug Your Cat Day.

June 3-9: Pet Appreciation Week. First week in June.

June 9: World Pet Memorial Day.

June 11: Just One Day.

Mid-June: Animal Rights Awareness Week.

June 24 [not confirmed]: Take Your Cat to Work Day.