One more use of series and parallel circuits I've seen is to provide very precise resistance or a resistance that isn't commonly available or that isn't economical to obtain in small values.
For example say you're manufacturing a device that uses large number of \$1 \mbox{ } k \Omega\$ resistors and for some reason you need few \$2 \mbox{ } k \Omega\$ resistors.
You could obtain as a separate part a \$2 \mbox{ } k \Omega\$ resistor and that would work well, but in practice the pick and place machines that put your components on a PCB can at one time place a limited number of different components.
One of the main points which assembly companies use when calculating price for assembly of a PCB is how many pick and place machines are needed to assemble a PCB and how long the assembly process is going to last.
The result of that is that you could save some money in product manufacturing by using two \$1 \mbox{ } k \Omega\$ resistors in series to get a \$ 2 \mbox{ } k \Omega\$ resistor.
Bulk purchasing comes into effect here as well. The more components you buy, the lower is the price for individual component. If you buy very large amounts of \$1 \mbox{ } k \Omega\$ resistors and only need a small amount of \$2\mbox{ } k \Omega\$ resistors, it could happen that two \$1 \mbox{ } k \Omega\$ resistors you place instead of a \$2 \mbox{ } k \Omega\$ resistor could be much cheaper than the single \$ 2 \mbox{ } k \Omega\$ resistor.
For precise resistance part, here a video that shows how such system looks like. There they basically made resistors using PCB tracks and then provided parallel connections between tracks and cut unneeded connections. This way, they can reliably make high precision resistors and solve the problem of manufacturing tolerances.
One more use is to distribute power over large number of components. Basic electronic courses often use ideal components and ideal resistor can dissipate unlimited power. In real world, current going through a resistor needs to be carefully set so that the power rating of the resistor isn't exceeded. A common way to do that is to replace an ideal resistor with a parallel network of real resistors.
Say for example that I need a relatively precise \$ 20 \mbox{ } k\Omega\$ resistor that needs to be able to dissipate 1 W. A local electronics shop I often use has \$ 22 \mbox{ } k\Omega\$ 1 W resistors with 5% tolerance for 8.5 US cents. On the other hand, it also has \$100\mbox{ } k\Omega\$ 0.25 W resistors with 1% tolerance for 1.5 US cents. So by using 5 0.25 W resistors in parallel, I can spend less money on the resistors and get a more precise resistor at the same time. Also don't laugh at the cost difference. Sure, for a small one-off project one cent may not be much, but on a larger project, where you'll probably make numerous savings such as this one, with a unit that will be manufactured in hundreds of thousands or maybe even millions, such every cent counts.