When you're arrested and charged with a crime, a record of the event is entered into the database that local and state law enforcement agencies use to monitor the criminal records of various members of the public. These databases can be accessed by virtually any American law enforcement agency that chooses to subscribe to them. These days, most major law enforcement agencies communicate freely with one another using these databases as well as other tools and resources.
When you're convicted of a crime, a record of your conviction will be entered into the database that's used by the jurisdiction in which you were tried. This will be a matter of permanent record and may show up on background checks conducted by prospective employers, security-clearance issuers, landlords, mortgage lenders and many other parties. Unless your criminal record is expunged by a judge, you'll live with this blemish on file for an extended period of time. Certain serious crimes like aggravated assault, rape and murder may remain on your criminal record on a permanent basis. Less-serious misdemeanors may drop off of your record after five, seven or 10 years. These reporting windows vary according the the policies of the jurisdiction in which you were tried and convicted.
It's very difficult to "outrun" your criminal history. Before law enforcement databases were widespread, it may have been possible to avoid full responsibility for past transgressions. Convicted criminals who moved across state lines could often avoid accounting for their crimes for years at a time. As recently as the 1970s, background checks were far less thorough and often produced glaring inconsistencies and information gaps. Convicted criminals felt little obligation to report their convictions on job, housing and security-clearance applications. Inter-agency information-sharing protocols simply weren't highly developed and couldn't keep up with an increasingly mobile population.
This has changed decisively. If you have a criminal record, it's now impossible to outrun it for any sustained period of time. Once you take up residency in a new state, your local motor vehicle bureau will be able to see all of the vehicular infractions in which you've been involved during the past several years. Once you apply for a job in your new home, the customary background check to which your employer will subject you is liable to turn up any record of past arrests or criminal convictions. Finally, you'll be at risk for arrest on any outstanding warrants that you may be carrying. These arrests typically happen during routine traffic stops.