Given how you posed your question, you may already be aware that the visual appearance of saturation is not always tied to a color's mathematical description of it's saturation. You can have a very saturated color, but it may appear mute if it has high luminance. Thus, vibrancy, or how saturated a color appears, is tied to it's brightness.
The most basic way of increasing vibrancy is to increase contrast in RGB mode. Because saturation is directly coupled with and influenced by the brightness of the RGB composite channels, adjusting contrast will cause less vibrant colors to become more washed out, while making more vibrant colors even more bold - incidentally while adjusting tonal contrast, you are also adjusting saturation contrast.
Adjusting saturation contrast makes an image appear more vibrant because the eye is drawn to more saturated colors over less saturated colors. By making areas of high vibrancy more accessible to the eye, we interpret the adjustment as an increase to vibrancy.
Having clean, desaturated hilights is probably the biggest thing that will help the appearance of vibrancy. We expect brighter regions to be desaturated, and having a color cast in the hilights permits them to compete for our attention with what the eye expects to be more vibrant.
Very few tools allow you to adjust saturation directly, without adjusting hue and luminance as well. One way to do this is to place a curves adjustment on saturation layer mode in an RGB color space, though this method is a bit kludgy and doesn't really work linearly.
Some tools do permit you to adjust saturation directly. Photoline32 does, and I believe that this is planned for GIMP in the future. Experimental techniques I've employed using Blender have also been very powerful. If you're interested in this approach, feel free to PM me for details.
What GIMP does permit is HSL decomposition, which splits the layers into HSL components, with the S component representing saturation. You can then apply a curve to this directly and compose the HSV image back into an composite color image. With practice, you could probably be able to predict how the results will turn out.
I can think up at least one other way, but it's weird and too complicated to describe here. Let me know if you're interested.
The other way to control vibrancy is through simultaneous contrast, which is how the eye perceives color when placed next other colors. For example, if you have a red object next to a blue object, adjusting the blue object to be even slightly more cyan/green will cause the red object to appear more vibrant.
I have also tried some approaches in HSL Hue Curves, by making warmer colors warmer and cooler colors cooler in increase vibrancy. This technique is subtle, but can work provided you don't get too carried away, it may also be carried out in Hue/Sat.
Simultaneous contrast is kind of a tricky subject, for which I don't have as much experience with. Every color has simultaneous contrasting pairs, so the technique can be applied in any situation. The issue is how it should be carried out and controlled. It's theory is pioneered by Josef Albers and is covered in his book, The Interaction of Color. For a very broad, technical understanding of this subject, I would recommend this book - not though, this is not a book on photography, digital or otherwise, but rather strictly about color theory.