Microsoft offers MSDE, the Microsoft Data Engine, which sounds like exactly what you need.
MSDE is a "workstation sized" version of Microsoft SQL Server. It offers a version of the database engine that is limited to 2 Gb per database, and is configured to run on a workstation (so it is missing a few of the really "high end" database features), that is 100% upward compatible with Microsoft SQL Server. It allows the developer to create databases that work on the desktop, can be scaled up to a few users (about 5) without any additional cost to either the developer or the user, and allow easy migration to SQL Server for larger groups of users.
While MSDE may not have the high end features such as clustering, replication management, etc., it IS a full blooded version of SQL Server. From the code perspective, it is almost impossible to tell MSDE from any other version of SQL Server. As your users needs grow, MSDE allows a quick and simple upgrade path to full-blown SQL Server. In almost every case I've seen, MSDE offers the best of both worlds... It is cheap and easy to start with, and can grow to support really large projects when necessary.
You will need to install MSDE on your machine (and install it with your software), and you get at least two files, an MDF with the actual data and an LDF with the log.
The MSDE software is available to Visual Studio Professional (and above) developers, and a license to distribute it as part of an application that you develop is included with Visual Studio. Think of MSDE as part of the Visual Studio runtime environment.
Check out the link to the article from my previous posting. I think that article gives the "30,000 foot view" of MSDE and the distribution model. The whole process really isn't very complex, although you need to think on a bit broader scale than you did with dBase files. Once you make the jump, you'll never want to go back!
I have just tried installing MSDE - when I double click the setup file, it says it can't install because I don't have a "strongpassword" on SAPWD... I go to the knowledgebase article they reference for help on this and do what is says, it says to enter oSQL -U sa at the command prompt and it says oSQL isn't recognised as internal or external command etc etc....
Check here for help with strong sa passwords from within code. As a general rule of thumb, just use a license plate or pick a sentence that you'll remember and take the first or last letter from each word to make a strong password.
Ok, I am running windows xp professional... I have downloaded the MSDE file and doubleclicked setup... when I do, it comes up with an error... that link you gave me was about setting with password once it has been installed... from what I could see anyway..