LEDs exist in various sizes ranging from very small to very large. Some larger high power LEDs, such as the Luxeon K2 and Cree X-lamp, feature a relativity large footprint. The K2 package is 0.470 inch by 0.337 inch, including the solder pads. On the other extreme, the 0603 package is so small it may be difficult to handle, with the bare hands. The 0603 package is only 0.06 inch by 0.03 inch dimensionally. Although the K2 or X-Lamp LEDs may be much larger, they also offer a much higher level of performance in terms of light output and efficiency. These larger LEDs may provide several hundred lumens of output, compared to the 0603 standard package which may offer less then one lumen of output. When you account for the space consumption and performance, it might make more sense to choose a larger LED package since its higher performacne allows it to utilize the consumed space more efficiently.
Certain lighting application may simply not offer the space needed for some larger LED packages. If a specific lighting application require a very small LED for any reason, one solution may be "Chip on Board". This technology allows one or several LEDs, to be packed into a very small space. This is made possible because chip on board relies on the bonding the LED die, the inner part of the LED, directly to a substrate. Each LED die may be only 1mm by 1mm, or smaller. There are also many disadvantage associated with the chip on board technology, making it unsuitable for many applications.
It is also important to consider the size of the required supporting components. Even though an LED itself may be extremely small, one must consider the size of the circuit board or substrate, electronic drivers, heat management system, and secondary optics. Combined, these required components can often consume much more space than the LED itself. A very simple configuration may consist of only the LED, a small FR4 circuit board and chip resistor as the driver. In this case, the circuit board also acts as a thermal management device, and the chip resistor may be as small as the LED. On the extreme end, you may require a large finned aluminum heat sink to mange your heat, and a network of electronic components as your driver circuity. This configuration could occupy many thousands of times the volume of the LED package itself.