LED's (and all other solid state diodes) have a property where the voltage drop across them will decrease with increasing temperature. If some sort of current control is not use, they go into a thermal runaway mode and self destruct. The simplest way of controlling the current is to put a resistance in series. When the current starts to increase, the voltage drop across the resistance increases, reducing the amount of voltage available to the LED.
The strip lighting which is becoming commonplace of late uses this technique. Typically, three LED's are connected in series and in series with the resistor. White LED's have an operating voltage window of about 3.0 to 3.5 volts so three in series gives a nominal voltage of about 10 volts. The resistance drops any remaining voltage. The strips that I have used will operate from about 11 volts to 14 or so with increasing current and brightness as the voltage increases. Somewhere above 14 volts, the LED's are being over driven, shortening their life.
LED's can also be operated on ac current, using their property as a diode rectifier. The now ubiquitous LED Christmas lights will series wire some thirty or so (for 120v.ac) without any additional circuitry.
Another method of driving LED's is using and active driver which contains electronic circuitry to set the drive current. This type of driver can typically operate over a large input voltage range. Some that I have used can have a 25 volt operating swing. Active drivers are also available in a boost configuration, where they increase the output voltage, and for operation on ac power, in which case the module has a built-in rectifier. Many of them also have provision for dimming, either internally or externally.
Bob