Since you can't do anything about the color management of other people's monitors, the best you can do is:

1. Make sure your own system is properly color managed (see other questions here on color management). That way, you are at least certain that you're starting from a known point. This is really worth doing even though it takes some effort and probably a small expense (which could perhaps be shared with a friend.) If you're hesitant to go down the whole rabbit hole, both Windows 7 and Mac OS X come with basic tools for visually winging it — better than nothing. (Or use http://displaycalibration.com/.)
2. Work in the sRGB color space. I know this seems uncool given that there are wider-gamut spaces with names like "Adobe RGB" or "ProPhoto" (and pro must be better, right?), but I find it best to work in the space that is the target. That way, you don't get surprises due to gamut clipping or shifts when you go to make your final output. (See note below.)
3. Save in sRGB. This is the defacto standard — that is, by industry agreement, it is the assumption that any uncalibrated setup should do a decent job of displaying sRGB images to a reasonable approximation of the original. Sometimes the approximation is awful enough to make color fanatics cringe, but that's the cruel reality of the world.
4. And then, make sure you look at your images in various web browsers on as many different systems as you can to make sure they're okay. Or at least approximately okay. Uploading to Flickr and looking at it there is exactly the right thing to do, if you expect the photos to be viewed on Flickr as the final presentation. To answer the "what software" question directly, the answer is the software that will be used in the end — a web browser.

Oh, and in case it the above doesn't make it clear, my guess as to what's going on is that your JPEGs (either originally from the camera or from a setting in the RAW conversion) are using a color space other than sRGB — probably Adobe RGB, since that's the most common alternative. The programs where the photo looks as you expect understand how to properly deal with that, and the programs where it looks wrong are rendering the data as if it were sRGB.

Footnote: If you're worried about working in the constrained sRGB color space instead of a wider gamut, keep your RAW originals. Then, you can redo this decision later for a different output medium. There are good reasons for the other color spaces and I don't mean to disparage them or their use. They're just not what you want here.