Take a look at some native third-party ADO components that will help you access databases with Delphi without the BDE. ADO is Microsoft's data access layer for relational databases, spreadsheets, email, documents, graphics and the Internet.
The Delphi ADOExpress/dbGO (D5/D6) components encapsulate the functionality of ADO objects and make them available in Delphi
Components for accessing, displaying and manipulating data in MS SQL Server, MS Access and other data sources through ADO. Includes RDS (Remote Data Service), ADOR, MIDAS and MTS support for multitier applications. Adonis compiles in to your EXE. With Adonis and Delphi you can access almost any form of data through a rapidly increasing range of OLEDB data providers.
GM-Components is a set of data access components for ADO and DAO, plus some database controls and other controls. These components compiles into your EXE. This package includes enhanced versions of many of the standard Data Control. For example, DB-Memo, DB-Image, and DB-Mediaplayer recognize drag-and-dropped Files.