No more guesses? How about some hints:
1776 is from a popular Japanese franchise, but this screenshot comes from the only one in the series to be released in the US. I also changed the screenshot to make the game more recognizable.
1777 is a Dreamcast game.
1778 is from the opening movie and is on the back box art of this game.
1779 I thought would be an easy one, so no hint yet.
1781 is a Sega CD game.
1783 is a strategy game.
1785 has a thread discussing it with over 100 posts in it on CAG.
1787 is the only Japan exclusive game in this set.
1788 is an arcade game from the 90s that got a Wii port.
1790 was released on multiple platforms in multiple regions and as far as I could tell, every release has the Statue of Liberty on the box art.