I don't understand your aversion to resistors. They are simple, cheap and very reliable.
If you're worried about efficiency, and circuit complexity is not an issue, you might want to look at Linear Technologies' LED drivers. (As an example; several other companies make LED drivers as well.)
The thing is, light output from an LED is related to the current through the LED, so the best solution is a current regulator (which most LED drivers are). Forward voltages have way too much tolerance for a voltage regulator to be very useful.
Remember, they're still diodes, and once they hit their knee voltage, small changes in voltage will mean large changes in current, and vice versa. If the forward voltage is 0.1-0.2 V off spec, it will mean a huge change in current (and brightness and power dissipation) to get to the regulated voltage.
The reason we use resistors so much is that they are way less complex than a current regulator, and very compatible with a regulated voltage rail. The idea is that you choose the current you want in the LED, and together with Ohm's law and the forward voltage, you figure out your resistor value. So long as the voltage across the resistor is much larger than the tolerance in the LED's forward voltage (1-2 volts is usually plenty), you'll get pretty repeatable results for brightness and current consumption. Don't forget to make sure the resistor can dissipate enough power (usually a problem for high source voltages or small surface mount resistors).