There are alot of ways to accomplish this. The simplest one is to use the sp_databases procedure. Here's some example that uses this stored procedure in conjunction with ADO.NET to consume the returned data.

The sp_databases procedure lists databases that either reside in an instance of the SQL Server 2000/2005 Database Engine or are accessible through a database gateway. You can read this article from MSDN for more information about the sp_databases procedure.

//######################################
//C# EXAMPLE
//######################################

//using SqlAdapter and DataTable
using (SqlDataAdapter adapter = new SqlDataAdapter("sp_databases", connectionString))
{
   adapter.SelectCommand.CommandType = CommandType.StoredProcedure;
   DataTable dataTable = new DataTable();

   adapter.Fill(dataTable);

   foreach (DataRow dataRow in dataTable.Rows)
   {
      Console.WriteLine(dataRow["DATABASE_NAME"]);
   }
}

//using SqlCommand and SqlReader
using (SqlCommand sqlCommand = new SqlCommand("sp_databases", new SqlConnection(connectionString)))
{
   sqlCommand.CommandType = CommandType.StoredProcedure;
   sqlCommand.Connection.Open();
   SqlDataReader sqlReader = sqlCommand.ExecuteReader();

   while (sqlReader.Read())
   {
      Console.WriteLine(sqlReader["DATABASE_NAME"]);
   }

   sqlReader.Close();
   sqlCommand.Connection.Close();
}

'######################################
'VB.NET EXAMPLE
'######################################

'using SqlAdapter and DataTable
Using adapter As SqlDataAdapter = New SqlDataAdapter("sp_databases", connectionString)

    adapter.SelectCommand.CommandType = CommandType.StoredProcedure

    Dim table As New DataTable()

    adapter.Fill(table)

    For Each dr As DataRow In table.Rows
    Console.WriteLine(dr("DATABASE_NAME"))
    Next

End Using


'using SqlAdapter and DataTable
Using sqlCommand As SqlCommand = New SqlCommand("sp_databases", New SqlConnection(connectionString)))

    sqlCommand.CommandType = CommandType.StoredProcedure

    sqlCommand.Connection.Open()
    Dim sqlReader As SqlDataReader = sqlCommand.ExecuteReader()

    While (sqlReader.Read())
        Console.WriteLine(sqlReader("DATABASE_NAME"))
    End While

    sqlReader.Close()
    sqlCommand.Connection.Close()

End Using

*btw, you can also do this by using SMO or DMO. Read this article for more info.