Well, I would note first that 19th century photographs show women of all body types. The corset was worn for respectability to a great extent, because it was just What You Did (similar to a bra today), and it also helped bear the weight of petticoats and heavy skirts. It smoothed the body as much as it emphasized the waist.

What if you were a super skinny Victorian woman with no boobs or hips? A corset has nothing to smoosh, so it wouldn't really help.

I'm not sure how much evidence we have of women using serious padding before the end of the 19th century - many 1840s-1880s bodices were fitted with thin pads over the side of the bust in order to smooth the fabric over the ridge of the corset - but we do have some extant "bust improvers" from about the turn of the century. I've also examined a wedding dress from 1896 that measures, IIRC, 21" in the waist and 26" in the bust inside some really sizable pads. Sahlin corset waists that do a lot more puffing out of the front of the bodice than reducing the waist appear around the same time. (Seriously, that's a hollow, stiffened form.) Early 20th century women also made use of corset covers decorated with lots of ruffles across the front to give bulk under a loosely-fitting bodice; here's a good blog post on the subject.

Hips were mainly irrelevant during the Victorian era - women were always wearing either layers of petticoats or a structure on their bottom halves that covered that area. However, in the 1890s these dwindled into thin pads or wire structures. Both padding and bust forms were a big part of creating the stereotypical Edwardian s-bend figure with rounded bottom and a low, heavy bust.

Likewise in the 1920s - what if you're super busty/curvy, and can't fit into a flapper dress because of huge boobs?

Later 1910s and 1920s fashion was really more about having a smooth cylinder for a body than skinniness, necessarily. Brassieres iwere often made of fairly solid materials, cut to minimize the bust rather than support it, and corselets and girdles also helped bring in the figure. Photographs of women in the 1920s show a lot of non-thin women who don't look awkward at all in their straight-cut dresses because they don't have too much boob or belly drawing the eye.

How do you cope if you're the wrong shape for the fashion of the time?

I hate drawing parallels to modern fashion because that can be a very unhelpful path, but it really is a lot like today. Some women changed their eating habits to try to fit the ideal. Some wore clothes that flattered their shape, even if they weren't on the cutting edge of fashion. Some used clever decorating or cutting in the way the clothes were made up to disguise "figure faults". Some just didn't care and went around in an unfashionable body. Lots of options!

The ideal body is just that, an ideal. The majority women never looked like the ideal body of their time the same way most modern women don't look like magazine models. Some women just didn't care too much about their appearance, but for those who did care they have a lot of resources to improve. For example here are many examples of chest binder ads from the 20's. Lane Bryant stores first opened in the early 1900's and became very successful in the next two decades because she caters to (in her words) "stout women" and made clothes not only in larger size but in flattering cuts. Even if you can't buy what you need in stores nothing is stopping you from making it yourself. Here are two example of handmade breast padding from the 1850's. Bustles can be considered an example of fake bums.

Primary source image for big hip/thighs in the 1920's. My pear-shaped Granny owned it and put fringe on them for good measure. (Missouri, late 1920's)