I forgot to mail in my 2016 State tax paperwork for IL. What do I do now? Can I still mail them or do I wait till I file my 2017 taxes?

You need to print them out...sign them, attach any tax forms, that show any IL withholding (like W-2 forms) and send them in to IL tax people by paper mail.  Include your payment if you owe IL some more $$, ANNNND Use a tracking method at the PO Service Counter.

NO......you cannot file them with your 2017 taxes.  Every year is considered separately .

You do not wait for the 2017 tax return to file the 2016 return.  Download the PDF of the 2016 tax return.  You will have to print, sign and date the tax return for mailing.  If you have a tax refund there is no penalty for filing a tax return after the due date.

To access your prior year tax returns sign onto the TurboTax website with the userID you used to create the account - https://myturbotax.intuit.com/

Scroll down to the bottom of the screen and on the section Your tax returns & documents click on Show.  Click on the Year and Click on Download/print return (PDF)