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. ) 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  that give results very close to my hand picking.
Mostly due to insufficient models of human perception of color. Our perception of color is not accurate, so picking complementary colors based on their actual wavelength will be less pleasing than picking complementary colors based on a perceptual model. I don't think any of the pickers you link to attempt this.
One attempt with libraries in a few common languages is HUSL: http://www.boronine.com/husl/syntax/#997061
A much older approach is described here: http://en.wikipedia.org/wiki/CIELUV
Learn more about color perception here:
[Edit: just noticed this was referenced by this comment below: https://news.ycombinator.com/item?id=7562905]
Not connected to the site except as a user.
I am curious, how would you approach generating a palette using these color spaces?
> how would you approach generating a palette using these color spaces?
This is exactly the problem I was trying to solve in creating HUSL.
You can think of HUSL as a version of CIELUV (Or, more specifically CIELCHuv, the cylindrical transformation of CIELUV) that is stretched vertically to fill in the 'holes'. HUSLp, the pastel version, is similar, but instead of stretching, it cuts the saturated colors off. (You can switch between them in the demo).
In fact, those stretching and cutting functions are the only thing that HUSL really does, the rest is all CIE math :P
Disclaimer: I'm slightly colour-blind - take with a pinch of salt :-)
So while the hue component isn't perfectly perceptually uniform, there is no way I could improve it without doing an actual study.
For web site palettes, I like to poke around on http://www.colourlovers.com for inspiration. http://colorschemedesigner.com helps with finding appropriately distanced colors that work nicely together (set colorspace to Opaltone colors to find a nice palette) and there is always http://www.colorhexa.com when I just want to quickly darken or lighten a color.
I am assuming you have a slightly different algorithm for these three, since the middle one doesn't seem to match the root color's brightness, and they seem to match saturation differently too. Make a choice between these before you generate, and if you want to eliminate this choice, I would go with the one that tries to match brightness/saturation as much as possible.
This caught my eye because I developed my own algorithm for this a few years ago and applied it to syntax highlighting.
I was primarily interested in an algorithmic approach to generating color palettes. I am familiar with the various tools available (Adobe Kuler being my favorite) that use color theory as a basis of providing colors to go with one that you've selected (i.e. complimentary colors, analogous colors, triadic colors). One the palettes that my app provides uses this approach.
Another approach I looked at was a trick that I've seen many designers use in which you "mix" a little of the color you want to use with another color. To play with this concept, I generate a random set of colors and blend it with the one that you've selected.
Finally, I am a huge fan of Gregor Aisch's work  with colors in regard to statistics. My third palette borrows a method of his that I had not seen elsewhere. He essentially maps a particular color space into two dimensions and keeps the third constant. You can sample equidistant colors along a line in that space to derive a set of colors that look good together. In my case I used HSL, where I hold Lightness constant (I use the value of lightness of the color you selected).
As he mentions in the post I've linked below, HSL is not necessarily the best color model to use this way. A more perceptually uniform color space like CIE LAB would be better. However, working with this space in this way is a little more complicated because, since this color space models how we perceive colors, it has holes. I had trouble finding an elegant way around those holes such that I could consistently offer a fourth palette.
Anyway, after looking at each of these methods, I was curious if any one of them would rise to the top as the favorite among users. Or, perhaps one method would perform better for some colors over others. I am in the midst of processing all this data and my thesis should be published within the next month. Thank you for helping me collect data!
One nice touch is that you can plug your own random RGB color generators that feed the optimizer, to find N distinct colors in a subspace of RGB. E.g., I use it to generate distinct pastel colors in visualization of linguistic data.
(I am not an expert in this topic, but I couldn't find a good Java library with solid theoretical underpinnings.)
Their theory page (http://en.wikipedia.org/wiki/Lab_color_space) goes into how they do it, it's a pretty interesting approach of pre-calculating using CIE lab and then hcl for display/ui.
And the ui is well done, too.
Beyond the color scheme part, another cool thing you can also do is find distances between colors using CIE_LAB specification. This is great for finding "like" colors on the fly.
I see you used Zerb Foundation, how did you like it I am thinking of using it on a side project.
Edit: Working in Chrome after a few refreshes.
I'm a big fan of Foundation, although if I wasn't trying to get this together so quickly I might have used something like Skeleton. But I'm sure that is another discussion thread entirely ;)