Phase Shift Keying: Is it ever actually used?
PSK is very much alive and used all over the place!

Let me correct a misunderstanding first:


  Or when PSK is talked about, is bandlimited PSK implied which amounts to QAM with a circular constellation?


Every communication signal is bandlimited. The constellation diagram has nothing to do with bandlimiting – that's job of the pulse shaping filter (this is an important theorem for digitall comms!). The constellation is what you see when you sample the pulse-shaped signal at the right instant, and what you multiplied with the pulses before shaping them.

Also, 4-QAM and QPSK are indistinguishable. They are identical. It's customary to draw QPSK with constellation points on the axes and 4-QAM with constellation points at odd multiples of 45°, but that's just a 45° phase shift, and phase is relative anyway. So, they are really identical.

Now, to the question, "is PSK used". Sure, all over the place!

Now, as Neil noticed, GMSK is very broadly used – GSM is indeed the most popular example! GMSK is indeed an O-QPSK system with minimal timing.

You'll find, to little surprise, that PSK systems are widely used when phase shifts don't change rapidly but magnitude might be very small or changing or generally, you'd want a fast AGC.

Satellite TV is one of these cases – I think DVB-S2 is still mainly uses QPSK. And seriously, digital TV has high data rates; so this is not a "toy example".

QPSK, 8-PSK and other modulation schemes are standardized modes for satellite telemetry modems(CCSDS 131.3-B-1).

Satellite telephony according to the GMR standard uses a \$\frac\pi4\$ QPSK variant, but you'll find that's really just two alternating QPSK constellations, one shifted in phase. 

The Differential (D) BPSK and QPSK modes are very popular with low-complexity systems, because you can avoid the need for phase synchronization there. For example, DAB / DAB+ are high-rate digital audio services (i.e. your next gen car radio will do that if you're in Europe), and they are heavily multicarrier systems (in fact, 2048-OFDM), but each of these carriers is DQPSK-modulated.

OQPSK systems (not only GMSK) are extremely popular in the automation sector: You'll find that IEEE802.15.4 (e.g. ZigBee) uses it as the default modulation. OQPSK is very elegant in that it has the simplicity of being QPSK (which has the simplicity of being 2× BPSK) with the benefit of not having 0-power crossings, and thus allowing for implementation of highly efficient power amplifier stages – so that your microcontroller with integrated ZigBee transceiver can work without an external amplifier, and with little battery use.

… and of course, there's thousands of RC controls that just do BPSK, because it's so simple, and still quite a bit more robust to noise than OOK of the same power. Or Wifi according to 802.11b (which uses QPSK chips, effectively). Or in fact, many spread-spectrum systems (GPS, some modes of UMTS).