Z Transform - Do i always need 2 poles for every "peak"?
If your system has a real impulse response, then pole &amp; zeros will be in complex-conjugate pairs; so a pole at $\omega = \pi/3$ implies another pole at $\omega = -\pi/3$ . 

Further, by the definition of poles, as the frequency $\omega$ get closer to the pole frequency, the frequency response magnitude increases (so as to say peaks!). So for every peak in the (positive frequency axis) then you would have at least two poles at the same frequency (one for positive frequency and one for the negative frequency). Note that there could be more, but at least two is required for a real system.

However note that, having $2N$ poles does not necessarily mean that the frequency response curve has $N$ peaks (sharp rising transitions). Indeed counter-examples are easiy to find, such as an Butterworth or elliptic IIR lowpass filters having no peaks, compared to a sharp isolated rising transition. 

Note that in those filters the poles are bundled together such that their indivual peaks have overlapping effects on the total frequency response (yielding a flat passband rather than isolated peaks).