Probably a very volatile topic. I'll chip in my thoughts.
You should probably see as many of the Top 100 Films as you can manage. I guess I've seen almost all of the AFI top 100.
http://www.afi.com/100Years/movies.aspx
You should probably see as many of the "cultural phenomenon" films of each era as you can - such as "Jaws," "The Breakfast Club," "Blade Runner," "Fight Club," "Goodfellas," "The Matrix," "Pulp Fiction," "Reservoir Dogs," etc. Some of these probably fall into film and cultural history category more than actual "great" filmmaking.
You should probably see as many of the AMPAS (Oscars) Best Picture winners as you can. These also might fall into the film and cultural history category, since they are also filmmaking industry political choices. I've seen most of those, as well. Quite a few are on the AFI top 100. If you follow a specific craft you should see as many of the Oscar winners in that category as you can; for me that would be Sound Editing and Sound Mixing. (BTW, I much preferred the "bake-off" format where
ONLY sound folks got together in LA to view/listen to all the Sound Editing & Sound Mixing nominees and voted on the sound categories. To me an award decided by your peers was definitely superior. This format was discontinued in 2006.)
http://www.oscars.org/awards/academyawards/legacy/best-pictures.html
Of course, you need to see the top Indie films, although this has been and always will be a hotly debated category.
http://www.filmsite.org/independentfilms.html
After that you need to see the better films in your genre.
My reasons are that these are "representatives" of the filmmaking "language."
I also believe that indie filmmakers especially need to watch older films - 30's, 40's, and 50's - since they were made without all of our wonderful technological toys, and $1 million and lower budget indie films just can't compete with the current hi-tech films, and must rely on story and characters as did those older films.