Of course, in most states it is illegal for a landlord to come over unannounced without due cause. However, asking to show up a week ahead of time just to check in on the residents and the state of the apartment are fully within your rights. This gives them enough time to clean up any excess mess that comes from living in an area while it means that you can still see any damage that may have occurred at the hands of your tenants. Pets, children, and even clumsy or possibly drunk adults can cause a good amount of damage in a short period of time and sometimes it can help to put your mind at ease just to see that your apartment isn't torn to shreds.
Many apartment complexes have inspection laws written into their bylaws, regardless of whether or not they enforce them. For example, my complex can enter my apartment for an inspection for anything from seeing if we have enough carpeting down to checking for holes in the walls. Most people have never had an inspection, but it also allows the complex to make sure that there are not too many people living in one apartment. It is rare, but the inspections do certainly happen.
For the most part, you will not need to do inspections on your rental property while someone is still living in them. However, you may want to be upfront and tell your new resident that they may occur. This should ensure that they will be more careful when moving around in your apartment.