I'm 25, and mostly enjoy movies from the 30s, early 40s, and late 90s. While many of my favorite movies, such as An Ideal Husband, Amistad, and Meet Joe Black, are from the very late 1990s (the only period that exceeds the early 1930s in my esteem), most of balance of the movies I like best were released during the Golden Age of Hollywood. (Indeed, I admire the late 90s and early 2000s in no small part because of the then-popularity of the Classical Hollywood Style which had been abandoned for decades.)
Some of my favorites from the Golden Age include My Man Godfrey, Goodbye, Mr. Chips, Holiday Inn, Thirty Day Princess, Manhattan Melodrama, They Died With Their Boots On, and Here Comes Mr. Jordan.
The period featured some of my favorite actors: Claude Raines, Sylvia Sidney, Cary Grant, Errol Flynn, Myrna Loy . . . I could go on for hours. Many of even the bit players in the best pictures were outstanding actors in their own right. I don't think Hollywood produced many stars of their equal until, again, the late 90s and early 200s, when a similar number of captivating actors were working again: Anthony Hopkins, Ben Kingsley, Ian McKellan, Judi Dench, Morgan Freeman, Lucy Liu, etc.
Another similarity, beyond the use of the "invisible" film-making style, that I've noticed between the very late 1990s and early 1930s is a subtle sense of approximate sexual equality that disappeared as both the 30s and 2000s progressed. Females in both periods generally wore more, were objectified less, and were treated as intelligent and focused on goals neither romantic nor sexual. The first version of The Maltese Falcon showcases this well, in comparison to the later two 1930s/40s versions of the story: Sam Spade's secretary in the first version is sharp-witted, conservatively dressed, and totally uninterested in him - which is not a plot point or even a visibly intended motif. The Bogart version of the picture is much more sexual and sexist. Like the comedic version of the picture (Satan Met A Lady), it features a ditzy secretary, higher hemlines, and female characters who pine for Mr. Spade. Altogether, the early 30s seem as much infused with the equalizing Republican spirit of the Progressive Era and Roaring 20s as the late 1990s are with the open and optimistic spirit of the Clinton period, which I'm quite fond of.
(I also enjoy the appearance of art deco architecture and decor in the early movies, especially in the rooftop dance scene in Follow the Fleet, having come to love it on Poirot in the 80s and 90s, which I didn't at first realize took place in the past.)