For example, in the 1940's, did clothing from the 1910's become trendy again for a period of time?
Oh, yes! Since the end of the 18th century, most fashion can be related to a retro trend, although sometimes the historical inspiration is kind of subtle.
Here's one that's more direct. In the 1850s through '80s, there was a Rococo revival in women's dress - most clearly shown in pointed waistlines and wide or bustled skirts, but also in naming silks and accessories after Mme de Pompadour and Marie Antoinette. (See Aspiring to la Vie Galante: Reincarnations of Rococo in Second Empire France by Allison Unru)
Then in the 1890s, there was a short revival of the early 1830s: compare the puffed sleeves and flared skirts of the 1830s with the puffed sleeves and flared skirts of the 1890s.
The slim and high-waisted dresses of the early 1910s were directly inspired by those of the 1810s - Paul Poiret introduced them in his collection called "1811". (See Poiret, ed. by Harold Koda and Andrew Bolton and Art Deco 1910-1939, Charlotte Benton, Tim Benton, and Ghislane Wood.) And then this era was revived in the 1960s, around the time of My Fair Lady.
Yes, just a few examples:
In the 70's the TV show Little House on the Prairie and clothing label Gunne Sax popularized Victorian prairie dress.
After the French Revolution Greek-style dresses and hairstyle became popular as a symbol of democracy.
Apparently, a large part of what made classical motifs so popular in federalist architecture was the rediscovery and excavation of Pompeii. All of a sudden, people knew exactly what wallpapers the Romans were using (don't question the part where the Romans wouldn't have had wallpaper, as middle class Bostonians didn't care). The arts & crafts movement was a shorter term retro craze in the 1900's meant to set aesthetics and society back to middle-class-artisan production rather than the contemporary dichotomy of cheap mass production and luxury good handmade by a master.
No, the Thirties/Forties were generally very new in style, with an occasion burp of antebellum in formal wear. The New Look, on the other claw, can be characterized as neo-Victorian: longer skirts, often w/tons of petticoats or a hoop, tight lacing and heavy corsetry, fragile femininity. There was a revival of Flapper fashion in the mid and later Sixties: not only the straight tank dresses with low band or covered in fringe, but a return of pin-striped suits. The Disco era thought of itself as picking up WWII elements, with the longer swirling skirts and Fred and Ginger dance styles. The Eighties had a serious revival of the Twenties hip band silhouette, as well as the return of the Swing era shoulder pad.