Lots of the details are found in the reference Reza provided, but in short . . .
STP is the granddaddy standard.
PVSTP variants are Cisco proprietary, and run a STP instance per VLAN, and may offer enhancements not found in the standard protocols. (NB: the advantage of "per VLAN", you can have different active links and/or different roots, for each VLAN.)
R(apid-)STP is a much enhanced version. Cisco's rapid-PVST is much like it, although it also supports a STP instance per VLAN.
MST, another standard, is basically rapid-STP enhanced such that you can define which VLANs are in MST instances. (NB: this too, like Cisco's PVST, allows you to have different active links and/or roots, but without the overhead of running a STP instance for every VLAN [often only one or just a couple of STP instances are really needed].)
CST is related to MST, it allows MST to inter operate with earlier STP standards. Basically, it "hides" MST multiple STP instances.
Generally, Cisco's current switches default using PVST+ (Cisco's PVST variants are proprietary), but they also support rapid-PVST and MST. If I remember correctly, the later PVST+ often provides optional enhancements, many of which are enabled if you enable rapid-PVST.
Generally, if using Cisco switches, you should enable rapid-PVSTP, unless you have a reason to configure MST.
