This acid yellow-green front door shouts "Come on in!" and works nicely with the natural wood siding. If you have no choice but to paint your siding, you could go with a cooler brown/taupe shade to set off the brighter hue of the door.
Example palette. Get a similar look with these colors (clockwise from top left, all from Glidden): Lime Sorbet GLG12 for the front door, Bronzed Ivy GLN23 for trim and Khaki Green ICI830 for the main house color.
I love this vibrant turquoise door against the dark sage-green house color. The white door trim makes it all look crisp.
Example palette. Get the same effect with (clockwise from top left, all from Martha Stewart Living): Lagoon MSL125, Lamb MSL225 and Bayou MSL237.
Orange doors are hot right now. Cool them down by pairing them with gray hues that have a bit of green in them.
Example palette: Try (clockwise from top left, all from Benjamin Moore): Tangy Orange 2014-30, Narragansett Green HC-157 and Templeton Gray HC-161.
One of my favorite colors, a bright leafy green, works well with steely gray neutrals.
Example palette: For a similar effect, use (clockwise from top left, all from Mythic Paint): Sweet Summer 069-5, Grecian Grey 132-5 and Court Magician 133-1.
Red doors look fantastic on just about every house style, from traditional to contemporary. Let the door remain the star by keeping the main house color neutral, ranging from white to cooler taupes or to gray. The cooler neutrals won't compete with the red, but instead will offer a nice, contrasting background.