Expunged convictions do show up on police databases. They do not show up on standard background checks. I know on presentence reports prepared in criminal sentencing, they pick up old expunged convictions, pleas under advisements, etc.
On the Canadian side, the RCMP fingerprinting service even has a special form you fill out for US Homeland Security authorizing them to release information about pardoned offenses. I am doing a friend's expungment and she had a funky entry about a marijuana ticket in Canada in the 1970s and I had to get one of these checks for the US Courts.
Look at your state statute, there are often statutory exemptions listed about who can see your expunged conviction. This often includes applying for jobs in law enforcement, applying for certain positions working with children, etc. I tell people to think of these adjudications as "sheltered" (e.g. partially protected) rather than eradicated. I know that our local CCW board sees expunged convictions as well. Additionally, US immigration law specifically says that a conviction that is set aside based on rehabilitation can still be considered in deportation proceedings.