Contrary to popular belief, extremely bright light often desaturates colors a bit. In theory, the brightness isn't what matters, but directionality does, and extremely bright light also tends to be directional. As a rule, you'll get brighter, more intense colors under a cloudy sky than under a clear sky.
There are (at least) two major reasons for this. The first is specular highlights. A specular highlight is where you basically have a direct reflection of the light source (in outdoor pictures, the sun) on the surface of an object in the picture. Pretty much by definition a specular highlight won't show any color -- a direct reflection of the sun will drastically overpower the filters in the sensor/film (and your eye) so unless you underexpose (quite a bit) it'll just show up as pure white. The more of these you get in your picture, the less intense the color will look.
The second is more about perception. In bright, directional light the ratio from highlights to shadows will be very high -- i.e., you tend to have very bright highlights, very dark shadows, and almost nothing in between. Under those circumstances, we mostly tend to notice the "bright" and "dark" themselves, and pay considerably less attention to the colors.
The picture above illustrates most of this reasonably well. Except for the white lifeguard stand, most of it is really quite low contrast. There's virtually no deep shadows at all, and the only thing close to bright highlights is the sand. Other than (again) the lifeguard stand, and probably a few of the waves, there's also almost no specular highlights.
John Shaw, for one example, points out that many of his "brightest" looking pictures were actually taken not only under cloudy skies, but when it was actually raining at least a little (though more than a little rain will reduce saturation at a distance very quickly).
Those can be controlled, of course. For many subjects, a polarizer can block a large part of specular reflections (especially useful for pictures with lots of vegetation). Water and (most) sand are quite reflective, which helps keep contrast more manageable for beach shots. Snow on the ground can do the same (even more so). Absent those, you can use reflectors to help fill shadows a bit -- at least for subjects that are reasonably nearby and small (it's not so easy to carry a reflector large enough to light, say, a mountain range).
Another crucial point is exposure. Overexposure can wash out colors badly. For maximum saturation, you may even want to underexpose a bit compared to the theoretically correct exposure. Here's an image with (simulated) overexposure:
The same shot with no adjustment to saturation at all, but correct exposure looks much more saturated:
You can re-process the first to get close to the second by doing nothing more than adjusting the levels in Photoshop (or whatever).