What are common restrictions for carry on bags and check-in bags at airports?

Here is everything you can and cannot bring in both carry-on and checked luggage:

http://www.tsa.gov/travelers/airtravel/prohibited/...

Things that need to go in your carry-on are money/credit cards, all forms of identification, any important documents, any prescription medication you may take, expensive electronics, jewelry, really anything of value/anything that is important and that you wouldn't want to have lost, stolen or damaged.

And to correct the post above me, you CAN carry on liquids, but there are rules you have to follow. You can find those rules here:

http://www.tsa.gov/311/index.shtm

The best thing to do is check with your airline, because some airlines have restrictions even beyond what the TSA has. The TSA website is the best place to start, but remember to check your particular airline, too. Especially check sizes of your bags. Some airlines will let you have bigger bags than others. If you are only allowed a tiny little bag, then there's obviously practically nothing you can carry on, even if it is officially allowed.

DO NOT bring sharp objects on your carryon, check that in.

You cannot carryon liquids either...

You can carryon your laptop, clothes(in a small luggage), books, camera. You know, small things.

You can pretty much check anything in.

the site of your airline should have all of this information, carryons and check ins can be a certain size. Depending on your Airline.