What colors are good to use for graphs and figures in scientific publications that print well in black and white?

In general using patterns is preferable than colour, especially for scientific papers. If you need to use colours though, I suggest you use a combination of high contrast colour values and limit them to two or three colours. For example in the figure below, I wanted to emphasize delayed activities for a Project. I used orange to highlight these values and shades of gray for the rest.

Shades of gray, come out well in print as well as photocopying. For screen viewing, black colours don't look attractive. If you expect people to view your paper on the screen (if for example you posting it on a web page) rather use colours and control the screen version via a boolean, but best option of course is to choose colors that look well both in print as well as on a screen.

I'd take a look at http://colorbrewer2.org/. It is a site designed to help pick color schemes for cartography, but I've used it to pick schemes for regular scientific plots as well.

There is an optional button that will only show color schemes that are photocopy-able. If you click on learn more it says:

Photocopy Friendly: This indicates that a given color scheme will withstand black and white photocopying. Diverging schemes can not be photocopied successfully. Differences in lightness should be preserved with sequential schemes.

An easy way to check whether the black-and-white version of a coloured document will be usable is:

\usepackage{xcolor}
\selectcolormodel{gray}