Visual Basic and Access were a great combination. They allowed the creation of small powerful apps, specially apps for data collection, or just applications that needed a small database that could run standalone.
A good option when you are upgrading your Access database and you do not need a centralized SQL Server (or that is just too much for your environment) is to migrate to other options like SQLite or SQL Server.
SQL Server has now a lot of versions (SQL Server Compact 3.5, SQL Server Compact 4.0, SQL Server Express and now even SQL Server LocalDB) a good table that compares this databases feature by feature can be located here: http://erikej.blogspot.com/2011/01/comparison-of-sql-server-compact-4-and.html)
If what you need is to support a simple, small (less that 4G) standalone database then using SQL Server Compact edition might be for you.
The main version for SQL Compact as at the moment 3.5 and 4.0.
Moving from Access to SQL Compact is not hard. There are many third party tools some free some not: http://erikej.blogspot.com/2009/04/sql-compact-3rd-party-tools.html
Primeworks tools are very easy to use, but you can also use the Microsoft SQL Server Assistant for Access (good links for this tools are in MSDN http://msdn.microsoft.com/en-us/library/hh313039.aspx and also the SSMA Blog http://blogs.msdn.com/b/ssma/)
SQL Server Compact uses the ADO.NET and OLE DB providers, and in many scenarios is just what you need. So take it as an option if you just need a replacement for MS Access