According to the substantial presence test I should qualify as a resident for tax purposes since I came to the US in 2006 with my children. However I am told that internatinal students must wait 5 years before they qualify. Which of these is right? I really want to claim my children - I pay a substantial amount for daycare each month and I have always filed as a single non-resident alien. Can I now file as a resident and claim my children?

I forgot to add that I am on an F1 Visa.

You do not qualify as a resident alien. You must file as a nonresident alien until 2011 (unless you change your visa status before then).

On F1 you are exempt from residency for 5-years. You must file non-resident tax return Form 1040NR or 1040NR-EZ and Form 8843.

Your income is not subject to FICA taxes but you must pay federal and state income taxes.
Read: Your U.S. Tax Return: U.S. Tax Filing Requirements for Non-Residents

Thanks! I guess this means that I cannot file a joint return with my spouse and that we cannot claim our children..

Correct.

If you are from Mexico, Canada, India or South Korea, you CAN claim your wife and children as dependents on Form 1040NR.