Can you try this?
SELECT [Title], [Firstname], [Surname], [Company_name], [Interest]
FROM [dbo].[EXTRANET_users]
WHERE CAST(Submission_date AS DATE) = CAST(GETDATE() AS DATE)
T-SQL doesn't really have the "implied" casting like C# does - you need to explicitly use CAST (or CONVERT).
Also, use GETDATE() or CURRENT_TIMESTAMP to get the "now" date and time.
Update: since you're working against SQL Server 2000 - none of those approaches so far work. Try this instead:
SELECT [Title], [Firstname], [Surname], [Company_name], [Interest]
FROM [dbo].[EXTRANET_users]
WHERE DATEADD(dd, 0, DATEDIFF(dd, 0, submission_date)) = DATEADD(dd, 0, DATEDIFF(dd, 0, GETDATE()))