Ohio law says that your landlord may enter your apartment to inspect the unit, make repairs, deliver parcels that are too large for your mailbox, or show the unit to repairpersons, contractors, potential tenants, or purchasers. Except in an emergency, or if it is impractical to do so, your landlord must give you reasonable notice before entering, and enter only at reasonable times. Twenty-four hours is usually considered reasonable notice.
As a tenant, you do have to let the landlord in if you receive the proper notice. But your landlord must be reasonable about coming into your apartment. For example, the landlord cannot demand to come in so often, or at such inconvenient times, that it has the effect of harassing you.
If you are a tenant in the City of Cleveland, and your landlord violates this rule, a City ordinance says that you may be entitled to recover actual damages (e.g. compensation for lost or broken items) or damages from $50 to $500, get an injunction preventing your landlord from entering your unit improperly, or terminate your rental agreement.