The spectrum goes from a carrier (delta(f +/- f0), to a modulated carrier. The spectrum around the carrier looks just like the modulation, i.e., if it's a square wave, then it has odd harmonics; if it's PRBS, it's pretty flat in the center, has a first zero around the bitrate (or is it half the bitrate, I forget), and looks like a sinc(f) spectrum beyond that (i.e., zeroes at harmonics of the bitrate, and humps inbetween).
QPSK has asymmetrical sidebands. This can be seen by interpreting it as the superposition of two (orthogonal) BPSK signals in quadrature; each one can be isolated independently, and each will have a BPSK spectrum. The sum will have harmonics above and below the carrier adding or subtracting, depending on the signal content, hence both sidebands must be retained.
QPSK can also be viewed as the superposition of several AM signals. The previous case is if the constellation diagram is aligned to 45 degree axes: amplitude in either the I or Q direction is constant for every symbol. If the constellations are aligned to the I/Q axes, then the phases are either the presence or absence of one or the other component, and therefore the sidebands of each I/Q component are identical to an AM signal of the same modulation (DSB-SC, to be precise).
So it shouldn't be surprising that all these modes (AM, PM, BPSK, QPSK) have similar spectra (i.e., all the signal energy within Fc +/- Fs, and repeating sidebands beyond there, which can be filtered off), with more subtle differences due to their nature.
Tim