The IRS has 10 years to collect. The clocks starts running on the due date or the date of filing, whichever is later. The clock stops ticking while the IRS reviews an Offer in Compromise or Due Process Hearing. Other events can stop the clock, as well.
If you own property, the IRS will slap a lien against the property. The 10 year statuette of limitation has no effect on the lien which follows the property until paid.
Most states do NOT have a statuette of limitation to collect.
OregonWino is wrong. The IRS has three years to audit you, seven if they have reason. In rare instances, the return is open forever. If you make a minor mistake on your tax return and the IRS doesn't catch it within three years, the return is closed.