There are several cases where a custom writen database application might be appropriate. For instance, if you run some kind of specialized store or service that doesn't have any software available to suit your needs or if you want your software to be tailored exactly to your needs but don't want to spend a fortune to do it.

Microsoft Access is the current database application of choice for us due to the low cost and realative ease with which the database can be accessed on the internet at a later date if so inclined.