A stand-alone database is the architecture that you are probably most familiar with. Like a word processor or a spreadsheet, all of the files associated with the application are all located on the same computer, and of-course the database system supports you - the user - very well. However, you will miss-out on one of the most useful features of a database, sharing data with others.
Microsoft Access is an excellent choice for stand-alone systems; where the data and the program to manipulate the data exist on the same computer.
Other Choices are Visual Studio .Net (pronounced dot-net), SQL server, Delphi, C++ Builder, Visual Basic and many others.