What causes the series resistance in capacitors?
I understand that caps have wires, which always have some resistance, but if wires are the cause of ESR, wouldn't all other wirings of the circuit usually cause much more resistance to be considered?


While the traces on your board are probably at least 20 microns thick (and maybe more like 50 microns), the metal layers inside an MLCC are probably only a micron or so thick. This means the resistance can be significant even for very short lengths of conductor inside the MLCC.

Also, the ESR doesn't only account for metal losses. It also accounts for any other power loss in the capacitor, such as dielectric loss. It's a simplified model for a lot of complex behavior, including other effects beside actual resistive loss.

However, there certainly are situations where you should consider your trace resistance in addition to the capacitor ESR.

On the other hand, if your concern is the self-heating of the capacitor and how much ripple current it can handle without overheating, then only the internal power loss, characterized by the ESR, is relevant, and the resistance of the traces connecting to it will have little impact.


  But let's consider electrolytic capacitors for example: The dielectric is an electrolytic liquid, shouldn't the liquid conduct electricity quite well?


If you used a liquid that conducted electric current well, you would have built a resistor rather than a capacitor. You must use a strongly insulative liquid rather than a conductive one to build a capacitor.


  Or if we consider ceramic caps: What causes resistance here?


There isn't much resistance. For an 0402 cap with a good dielectric, it might be in the 10's or 100's of milliohms. But the resistance isn't zero, and it's high enough that we need to consider it in many circuits, so manufacturers find they get more customers if they specify it.