That depends on state laws. Commonly, a landlord is only allowed to enter a unit they rent to the tenant for their exclusive use for an appropriate reason at reasonable times with reasonable notice. Rules are likely to be different for situations like short term transient housing or boarders. Some jurisdictions may, or may not, let the tenant explicitly grant the landlord more access in the contract.
Remember, the landlord rented or leased the property to the tenant for the tenant's use - by doing so, the landlord has relinquished some control and use of the property in exchange for valuable consideration (the rent!). It's not unlike a dealer leasing a car to you for three years - as long as you make the payments and comply with other aspects of the contract, the dealer can't just decide one morning that he's going to use the car for a couple of days to haul steer manure from the nursery without your permission "because it's his car".
Appropriate reasons for entry include maintenance and repairs either initiated by the landlord or by the tenant. An annual inspection or showing the unit to prospective tenants or property buyers may be an appropriate reason. But the courts in jurisdictions I've lived in would be unlikely to consider weekly inspections of a residential property leased to the tenant for one year to be appropriate barring some extraordinary circumstances.
Reasonable times may be only during business hours or from 8AM to 6PM or something like that for non emergency cases - for true emergencies like a major water leak, any time of day or night is probably usually reasonable.
Reasonable notice varies, but for non emergencies, some jurisdictions require 24 hour written notice. Again, for true emergencies, no notice may be required beyond a knock on the door.
Check your local laws -- some regions are much more "tenant friendly" than others and the laws vary quite a bit across the US.