While state laws and insurance company guidelines however in general if you are in an accident with expired license plates (tags) but not at fault you can place a claim through the at-fault party's auto insurance.
Normally your rights to make an insurance claim as well as your own insurance contract is still in effect regardless of license or tag status. Unless there is an exclusion in your policy then likely your car insurance would be in effect even if your registration is expired and also you would be able to make a claim through another person's liability coverage.
If you were ticketed for driving with expired registration then you would need to take care of that citation by contacting the court listed on the ticket.
If you have let your plates expire, many states have grace periods so see if you can get them reinstated and up to date without a penalty by checking with your Department of Motor Vehicles. If you do so before your court dates, if you were cited, then it may help you get the ticket dismissed or reduced.