Articles of Incorporation
The processing time of filing of Articles really depends on the state, and the time of the year (as this industry is in a way seasonal). Most states have official processing times, ranging widely from just one day to a couple of months. In other states its possible to look up current processing times at any given day, or call the Secretary of State and ask how long it takes them to process applications nowadays.
Also, during January, February and first half of March it usually takes the states a bit longer to process applications. Keep in mind that many states offer expedited service for additional fee.