For my latest side project, I needed sets of up to 5 colors that go well together but are sufficiently distant not too be confused. Since this is the task that palette generators typically set out to achieve, I tried a couple of them [1,2], as well as some "hand crafted" palettes found on design blogs [2,3]. In each case, I found that the palettes, while satisfying the desired properties, were aesthetically not particularly pleasing, in a sense lacking a unifying quality.
Thinking that "picking colors that go well together" must be a solved problem, I resorted to looking up photographs of 20th century paintings (e.g. [5]) and using the color picker in Gimp to extract what I visually perceived as the most important colors. This gave me far better palettes that any of the generators.
There are ways to do this algorithmically, as a form of constrained color quantization, and I later found online implementations as well [6] that give results very close to my hand picking.
[1] http://colorschemedesigner.com/
[2] https://www.colorschemer.com/online.html
[4] http://niklausgerber.com/blog/flat-ui-color-autumn-edition/