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If a diode is forward biased in a circuit it does indeed absorb some of the power. It kind of acts as its own resistor. That is why you have to determine what wattage the diode will be. It will drop about 0.6 volts but will pass all of the rest of the voltage. Diodes are used in power supplies all the time and do not have series resistors anywhere in the circuit.
However, if you are talking about Light Emitting Diodes, LEDs, then you have to but a resistor in series to prevent the current from burning out the LED. LEDs are not used or wired in the same fashion as regular diodes. They are similar in function but have dramatically different uses.
For a forward biased silicon diode ,the forward voltage required is 0.6 V .Now if we are providing it with around 5 V supply,it will quickly burn out without the presence of a passive element in the circuit. The presence of a series resistor which is known as the current limiting resistor prevents this and dissipates the extra power and ensures the proper functioning of diode.
In forward bias, diode offer very less resistance i.e few hundred ohms. When you apply say 5V and resistance is 1k than current will be 500mA and power dissipation is I^2 R. A small diode can't dissipate that much heat and will burn soon. So a resistance is series is connected to limit current through diode. Hence called current limiting resistance.
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