Access' big advantages:
- It's nearly ubiquitous
- It doesn't cost much
- You can easily package the application with the DB
- Speed of development
Big disadvantages:
- Multi-user situations
- Ease of corruption
- And ... sometimes packaging the application w/ the DB actually trips you up. Like when you have to roll out a code change to existing customers ...
I like Access for applications that are relatively small & simple and have few users.
For anything approaching Enterprise-grade, I would write either a Windows application and tie it to an MS SQL Server (possibly Express) DB, or write a web application tied to either MS SQL Server or MySQL.