Why do convex lenses not disperse light like prisms, given that entry and exit points aren't parallel?

They do. It's called chromatic aberration - each different frequency has a slightly different focus point, blurring the image by different amounts for the different colors. Modern lenses of high quality have multiple elements added specifically to address the issue of chromatic aberration.

What happens with flat glass isn't chromatic aberration - that's an illusion from working with geometric optics. Basically, to get chromatic aberration the rays of light have to exit the glass at different angles, which doesn't happen with glass that is flat on both sides.

It's helpful to think of it in terms of the wave fronts instead of the ray paths, because that is closer to the physical optics. The glass messes up the phase relationship between waves of a different color, but our eyes aren't sensitive to that, anyway. A spherical wave front on one side will be spherical on the other, for all colors (same for flat). All spherical wave fronts that share a center on one side of the glass will also share a center on the opposite side.

What, effect, then, does the displaced ray paths through the glass correspond to? Well, I haven't done the math on this one, so take it with a grain of salt, but I'd bet what it means is that the light that has more spread out ray paths will be dimmed more by the glass than the light that isn't.

Sean E. Lake's answer is right: convex lenses disperse light like prisms and that effect is known as chromatic aberration - which is easily noticeably by zooming in in the corners of photographs taken with cheap cameras.

I would add to his answer the reasons why usual convex lenses disperse light much less than a prisma does. For example, it's difficult to project an spectrum using a pair of common eyeglasses, a magnifier or even a photography objective.

The first reason is that lenses are usually thin, and therefore their sides are nearly parallel - at least compared with a prism. Dispersion is very related to angle between faces, and lens faces are just a few degrees apart while in a prism they could be at 60º.

The second reason doesn't hold for simple lenses (like eyeglasses or magnifiers) but holds for more complex systems equivalent to a convex lens (like photography objectives): lenses are combined in a way that most of their chromatic aberration get cancelled.