actually … adobe's  media-player(ver 1.8)  seems  to  have  the  feature  being  discussed.  person  can  watch  one  video  and  select  "pause" … close  program  or  quit  program  from  system-tray … even  switch  to  another  video … when  you  return  to  that  previous  video,  it  will  resume  where  it  had  been  paused.  i  should  explain  a  bit  further … the  videos  i  tried  were  on  my  hard-drive  and  were  located  in  my  "favorites/personal-videos"  within  the   program  interface.  have  att'd  screen-cap  for  clarification  of  adobe's  interface.
edit:  wanted  to  add  one  other  suggestion.  be  cautious  when  downloading  the  software … copy/paste  the  url  to  virus-total  website  so...