For what purpose would you keep them? If you are self employed, I believe you have to keep them for 5 years if they are a business expense. If not, check the next bill is correct against the last one, and chuck the last one, always keeping only one bill.
For privacy and security sake, don't chuck it away, destroy it. A "recent" utility bill can be used as I.D. for fraudulent purposes. Better safe than sorry...
A few years ago the ESB arrived at an elderly relative’s house to cutoff his electricity. Luckily he had still had the last few bills to prove they had been paid!
ESB bills etc should be destroyed. In the days of ESB shops it was possible to walk in and buy good on the never never, just using a bill as ID.
Not self employed, but thought I should keep some of them in case of problems (e.g. they claim I haven't paid, etc) Had problems with ADT (monitored alarm) in the past, they were overcharging and refused to reprint bills. Luckily we had copies