I use vinegar to clean everything. It's cheap, safe and very effective (for cleaning tips and uses go here).
However, my husband loves bleach. It's more of an obsession, really, but he uses the stuff all the time in the kitchen. I tell him frequently that vinegar does the same thing without filling our house with fumes, but he wanted me to prove it.
Hubby, here you go.
Does vinegar kill bacteria? According to WikiAnswers,
"Yes, vinegar DOES kill many bacteria and viruses, including many very dangerous ones that can be in food such as E. Coli O157:H7 (see for example scholarly research that shows this http://www.ingentaconnect.com/content/iafp/jfp/1998/00000061/00000008/art00005 ). It is probably good to use in the kitchen and other places that you may be worried about harsher chemicals like bleach getting into food."