How to query a MS-Access Table from MS-Excel (2010) using VBA

Sub Button1_Click()
Dim cn As Object
    Dim rs As Object
    Dim strSql As String
    Dim strConnection As String
    Set cn = CreateObject("ADODB.Connection")
    strConnection = "Provider=Microsoft.ACE.OLEDB.12.0;" & _
        "Data Source=C:\Documents and Settings\XXXXXX\My Documents\my_access_table.accdb"
    strSql = "SELECT Count(*) FROM mytable;"
    cn.Open strConnection
    Set rs = cn.Execute(strSql)
    MsgBox rs.Fields(0) & " rows in MyTable"

    rs.Close
    Set rs = Nothing
    cn.Close
    Set cn = Nothing

End Sub

The Provider piece must be Provider=Microsoft.ACE.OLEDB.12.0 if your target database is ACCDB format. Provider=Microsoft.Jet.OLEDB.4.0 only works for the older MDB format.

You shouldn't even need Access installed if you're running 32 bit Windows. Jet 4 is included as part of the operating system. If you're using 64 bit Windows, Jet 4 is not included, but you still wouldn't need Access itself installed. You can install the Microsoft Access Database Engine 2010 Redistributable. Make sure to download the matching version (AccessDatabaseEngine.exe for 32 bit Windows, or AccessDatabaseEngine_x64.exe for 64 bit).

You can avoid the issue about which ADO version reference by using late binding, which doesn't require any reference.

Dim conn As Object
Set conn = CreateObject("ADODB.Connection")

Then assign your ConnectionString property to the conn object. Here is a quick example which runs from a code module in Excel 2003 and displays a message box with the row count for MyTable. It uses late binding for the ADO connection and recordset objects, so doesn't require setting a reference.

Public Sub foo()
    Dim cn As Object
    Dim rs As Object
    Dim strSql As String
    Dim strConnection As String
    Set cn = CreateObject("ADODB.Connection")
    strConnection = "Provider=Microsoft.Jet.OLEDB.4.0;" & _
        "Data Source=C:\Access\webforums\whiteboard2003.mdb"
    strSql = "SELECT Count(*) FROM MyTable;"
    cn.Open strConnection
    Set rs = cn.Execute(strSql)
    MsgBox rs.fields(0) & " rows in MyTable"
    rs.Close
    Set rs = Nothing
    cn.Close
    Set cn = Nothing
End Sub

If this answer doesn't resolve the problem, edit your question to show us the full connection string you're trying to use and the exact error message you get in response for that connection string.