First of all, could it be that the original title of the thread was meant to be Best Era/Movement in Film (History)?
Anyways... some time ago I probably would have answered like R6dw6C, and I still think that the majority of the most interesting films I've seen have been made during the 60s and early 70s. But thinking about it now, I'm not so sure that quantity and diversity really get my vote. Otherwise i would also have to consider wpqx's choice, though I would never limit it to the United States. 1929 - 1933 was an incredibly innovative and interesting period for films all over the world. I love early sound and camera experiments (Films like The Front Page, Little Ceasar, A nous la libert, M, Frankenstein, Dezerter, Entuziazm, Kameradschaft come to my mind), and I want to see more.
But if I listen to my gut feelings, there are three time periods I currently find most interersting.
On top of my list would probably be the period roughly between 1909 and 1914/1917 (depending on whether films could be produced during WWI in some countries). The evolution of the medium was undergoing many shifts, and the co-existence of short and epic films (ranging from ten minutes to four hours) and the incredibly diverse stylistics of many companies, not to speak of the individual national preferences was very interesting. I think that there was probably never a time when films were speaking with as many diverse and interesting voices as in those times before the war. The amount of films produced is also incredible, and the fact that directors or actors were either the focus of a film or not important at all (nevertheless this was a real period for an auteur theory imho) is particularly interesting. It also seems like mostly national films were most succesfull in each country and there wasn't a clear stylistic or a mainstream to follow. So many thing changed in a period of 5 years that it seems incredible. Unfortunately not many films from this very important era survive today.
Another candidate would be 1918 till 1928. From what I've seen this is the period from which I enjoy most films. That doesn't mean that I like most films I've seen from the time or that I've seen many great ones. It has probably more to do with the fact that I love the stylistics of silent cinema, and it seems that in this period silent films were "ultimately" defined as how they are largely seen from today's perspective. Films entered the modern age, and movements were blossoming all over the world as (American) cinema was deciding an aesthetic assumption of how a proper film had to be made. I think there were never as many movements and trends in such a short period of time (expressionism, impressionism, surrealism, poetism, naturalism, the soviet film theories, etc.) while there was seemingly less and less experimentation in mainstream productions, which finally materialized as we know it today. I enjoy the conventions of those times as much as the innovative work. Unfortunately the whole medium was rethought with the breakthrough of sound in 28. I would have wished for at least 5 or 10 more years of silent cinema.
The third contender for most interesting era in film are in my opinion the 1980s. Yes, you are really reading this from me - the much loathed consumerist, superficial, vacuous 80s that brought us Reagan, Thatcher, Yuppies and the Porn industry as we know it today, the time when Pop Music seemingly made some last hopeless breaths before degenerating into the mindless trash of the 90s. It seems like "globalization" and its negative effects we witness today really got a boost back then, but -
If I look at the films made during the 80s today I find much innocence even in the dumbest of commercial products in a way that is totally lacking in today's mass production of mindless junk. And if I roam through the forgotten or unknown artisitc waters of those times I uncover as many great films and filmmakers as in any other area. The only problem seems to be that only few people seemed to care about those, and I completely cannot understand why all the excellent films weren't hailed as enthusiastically as many products of the various new waves during the 60s. It seems that the people (and critics) actually tried to purposefully dumb down their lives because of the socio-political changes during the 70s. If I think of films like Ken McMullen's Zina (1985), Straub and Huillet's Klassenverhaltnisse (Class Relations / 1983) or mamoru Oshii's Tenshi no tamago (Angel's Egg / 1985) they are as interesting experimental and daring as narrative films can be. And we also have Chris Marker's Sans Soleil (Sunless / 1982), Andrzej Zulawski's Possession (1981), Jaqcues Doillon's La Pirate (The Pirate / 1984) or La vie de famille (Family Life / 1985), Frank Beyer's Der Aufenthalt (The Turning Point / 1983), Jerzy Skolimowski's Moonlighting (1982), Sogo Ishii's Bakuretsu toshi (Burst City / 1982), Olivier Assayas' L'enfant de l'hiver (Winters Child / 1989), Mohsen Makhmalbaf's Arousi-ye Khouban (Marriage of the Blessed / 1989) or Bicycleran (The Cyclist / 1987), Abbas Kiarostami's Khane-ye doust kodjast? (Where is my friends house? / 1987), Margarethe von Trotta's Rosa Luxemburg (1986), Isao Takahata's Hatoru no haka (Grave of the Fireflies / 1988 ) , Hayao Miyazaki's Majo no takkybin (Kiki's Delivery Service / 1989) or Tonari no Totoro (My Neighbor Totoro / 1988 ) , Patrice Leconte's Monsieur Hire (M. Hire / 1989), Leos Carax's Mauvais sang (Bad Blood / 1986), Jean Jacques Beineix's Diva (1981) or La lune dans le caniveau (The Moon in the Gutter / 1983), Tian Zhuangzhuang's Dao ma zei (The Horse Thief / 1986), Chia-Liang Liu's Wu lang ba gua gun (Eight Diagram Pole Fighter / 1983), Samuel Fuller's The Big Red One (1980), Maurice Pialat's Loulou (1980) and the three incredible feature films by Emir Kusturica and Peter Greenaway. And how about Jim Jarmusch or David Lynch?
I'm not even talking about the (late) works by established masters like Fellini, Kurosawa, Scorsese, Svankmajer, Angelopoulos, Resnais, Rivette, Varda, Godard, Fassbinder, Wenders, Herzog, Kubrick, Tarkovsky, Bresson, and who else and I still haven't mentioned any of the Hollywood gems (Heaven's Gate, Eyewitness, Pennies from Heaven, Blade Runner, Conan the Barbarian, Victor/Victoria, Scarface, The Hunger, The Terminator, Back to the Future, Ferris Buellers Day Off, The Princess Bride, The Accidental Tourist, The Unbearable Lightness of Being, Batman, to name but a few).
I know I've still forgotten too many (Claire Denis, Catherine Breillat, Zhang Yimou, Luc Besson spring to mind) although I've only seen very little from the vast amount of films that were made in the 80s. If somebody is complaining about the poor state of (World) cinema during those times, I simply have to say: look again! If this is poor, give me poor every day