What components can be placed not to close to the circuit like capacitors and still work fine?
Any component that has a high impedance can generally be extended by arbitrarily long wires, with only an increase in its impedance. So the effective value of the component will change slightly, but not the way it's expected to work. Sometimes capacitors are used in a high impedance mode for signal coupling, when the same applies.
Often capacitors are used for their low impedance when decoupling power supplies. Then any finite lead length degrades their performance.
Before you can answer whether long leads are permitted, you need to know how you are expecting the component to work in the circuit.
Long leads can also get us into trouble, regardless of the type of component that their extending.
They can enhance capacitive or inductive coupling between different parts of the circuit, and can make amplifiers unstable or degrade filter stopband performance.
A long lead can inject current into a part of the circuit remote from where it's being sourced. This current flowing in the board's return path can couple signals to other circuits, again causing problems in circuit operation, possibly even at DC.
You can see the effect of impedance in the fact that industrial control systems, at least the old analogue ones, use 4 to 20 mA current loops, where the sensor operates as a current sink, drawing a current related to the process variable. A current sink has a very high, ideally infinite impedance. As a result, such systems can work reliably over open wires of many hundreds of metres, sometimes kilometres, in length.