Well, many very common circuits utilize the difference in W to achieve different objectives.
For e.g. In a current mirror, the output current is equal to input current times the ratio of W's of output and input transistor.
Similarly, many a times we want to have different W's to have different gains (transconductance).......also when you want to use a small capacitor in your design, you simply short-ckt. the drain and source, thus you have a two-terminal device that can be used as a capacitor whose value to be adjusted using W.
In most circuits, we want to keep L the same (minimum value), because if L is larger the path of the charges in going from drain to source increases, slowing down the circuit. However, still we do have some special-purpose circuits, that utilize higher values of L; for e.g. to increase the delay (when we intentionally want a delay)....You must keep in mind that going from one technology node (one particular Lmin) to another technology node (one with a small Lmin), is a very costly business. The reason we keep trying to decrease L, is to achieve higher speeds and less power consumption. Thus, when working with a particular Lmin based technology, you want to use that Lmin for most of the transistors in your design.
HOPE THIS HELPS.