It depends on what they earn and agree upon. Most newly "living together" couples operated financially the same way as roommates when it comes to paying the rent. They split it right down the middle. Some also do this with utilities as well. In other instances they agree to sort out the utilities. One person may take over the TV cable bill while the other takes on the electric or heating bill.
There is no hardcore rule as most couples try to find out what works best for them. The one thing I would avoid is establishing any joint financial bank accounts or requesting additional credit cards under each other's account. Don't risk your credit rating by adding others.
You can only control your spending habits. If someone bounces checks or runs up credit expenses on (your account) you are held responsible in the end. I've seen relationships end but the effects of bad financial dealings last several years after the breakup.