What can happen to me if I don't file my taxes multiple years?

Owe a lot of money, go to prison, get a tax lien on your bank accounts, home, cars, what else bad do you want to happen.

So you go back and file for all the years you did not, does not mean you write a check, but you file, After that you work out a payment plan with them

You must file all the tax returns if the income was more than the filing requirement.
For returns for 2005 and previous years, you will not get any refund even if you have a refund.
If you owe taxes, you must pay with interest and penalty.