I have two bills that I have to write a check for and it irritates me. One requires me to have a savings account with them in order to pay online while the other charges a $7.95 convenience fee to pay online.
Basically yes, its safe to pay bills online. Just make sure the page is encrypted and that YOU put in the URL so you know exactly where you are. Do not make a central username and passwords for all sites, just write them down and keep them safe.
I went from spending an hour or so writing out checks, updating bills, filling out envelopes and mailing them to maybe 10 minutes logging into the sites and paying directly and updating my money software.
Been paying online since 2004 with everything I could and the only identity theft I have had was with a stolen check so to me, paying online is safer and easier, and cheaper.