Usually no, although in some cases you may be able to dump fuel by exploiting features of the fuel system. Why not on smaller planes? Fuel jettisoning systems were only ever required for transport-category aircraft. There is some reasoning behind this link, since many transport category aircraft perform comparatively poorly at MTOW and would take a long time to burn off the difference between maximum take-off and maximum landing weights. Many GA aircraft can even land at their maximum take-off weights and so don't list a separate landing weight. (See, for example, the C172 POH)
The reason for this discrepancy between small and large aircraft, like many differences between transport category and GA aircraft, is in part due to practicality and in part due simply to regulation. Fuel jettisoning is required on many transport aircraft but is not required on GA aircraft. The FAA had a regulation that stated (though it's since changed to be performance, not weight-based):
Sec. 25.1001 Fuel jettisoning system.
(a) If the maximum takeoff weight is more than 105 percent of the
maximum landing weight, there must be a fuel jettisoning system able
to jettison enough fuel to bring the takeoff weight down to the
maximum landing weight...
version of 25.1001 effective on 02/01/1965.
There is good reason for the distinction between small GA aircraft and large transport aircraft in certification requirements. First, many GA aircraft are designed to be able to land and take-off at the same weight. Other reasons include performance consideration and that fuel flow is not proportional to max fuel, in part because larger aircraft usually have longer ranges. Longer range means more distance to burn off all the fuel, which usually makes it harder to burn off any unwanted fuel.
If you want to be technical, the driving factors here are the performance at MTOW and the practicality of burning off the difference in MTOW (max takeoff weight) and max landing weight, not fuel fraction (fuel available/empty weight) and not necessarily the ratio of MTOW to max landing weight. As counterexamples to the notion that fuel fraction or MTOW/MLW are important, the F7x can hold almost 90% of its empty weight in fuel but can also land at almost 90% of its take-off weight and so has no fuel dumping. Even a Learjet 60XR, with a MTOW to MLW ratio worse than an A320, can burn off the difference in fuel during a little more than a 300 nm trip. By comparison, by my calculations a 757-200 could make a 2,000 nm trip without burning off the difference between maximum take-off and maximum landing weights, and circling for hours burning off fuel like that tends to horrify passengers. (Source: Plane Purchasing Handbook 2012 and this 757 presentation).
You may also want to read: Why doesn't the 737 have a fuel dump nozzle? and When are aircraft required to dump fuel for emergency landings?