My twopence...

   Ex-felons, ex-offender, one that spent a year (two years etc) in prison, someone that had a stint in jail/the big house etc.

   Somebody with a criminal record:

   "I am a Florida man, 43, American, with a criminal record."
  (in this case it might date back to years ago, might be felonies and misdemeanors, or even crimes of theft or violence or some more serious issue , then one might be dismissed or convicted.)
 

  http://en.wikipedia.org/wiki/Convict

Ex-convict (or short: ex-con) is a common way of referring to a person who has been released from prison.

   Hope it helps...