In D&D 3.5 Prestige classes were great. Maybe a little too great. There certainly a bazillion of them. It was a different design philosophy. Base classes tended to front load abilities and Prestige classes tended to be stronger than base classes so it made no sense not to multiclass into a Prestige Class. Some of the results made no logical sense (story-wise) but from a power-gaming point of view they were the only way to go.
Pathfinder changed things up a bit. The base classes were improved, giving players a reason to stick with the class over all 20 levels. Archetypes were introduced for more variety, but Prestige classes were not really changed. They certainly were not improved and in many cases they were made worse.
Looking back at all of the PCs I've seen since we started playing Pathfinder, there have not been too many Prestige classes in use. A little bit of base class dipping here and there but I would say in general people are sticking to one class. Prestige class usage is quite rare.
Let's take a closer look at the Prestige Classes (PrC) in the Core Rule Book and see why.
Arcane Archer: This PrC did get buffed a bit and had its racial restrictions removed. Its actually not bad. Its great for an archer that wants to dabble a bit in magic. Most of it abilities are mutually exclusive and not terribly useful. It is a cheap way to get Fire or Holy on your arrows and get a few spells while keeping full BaB.
Arcane Trickster: This one looks awesome until you actually play it. You can sneak attack with spells! That sounds awesome until you realize that your BaB is so terrible touch attacks are your only option if you want to hit anything. Then we have the problem of doing ranged sneak attacks. The easiest way to do sneak attacks is with a flanking buddy which won't help you since spells don't threaten. Luckily at some point you should get Greater Invisibility which is great but you are getting it quite a bit later than a straight wizard would. Then you realize that sneak attack really isn't that much damage anyway if you are only doing it once per round. You quickly realize you are probably better off to play a wizard if you want to be anything other than super sneaky and a Rogue or one of its better variants if you do.
Assassin: why is this even in the Core Rule Book? It is a NPC class. Most of its abilities are of little use to your typical PC. It pains me to type this but even the Rogue is better than this garbage. Assassin is a cool class name though.
Dragon Disciple: I always see lots of interest in this PrC but I can't figure out why. It looks great with lots of attribute boosters but then you actually try and build one and you quickly realize that it is a little bit of everything that adds up to nothing. The entry requirements scream Sorcerer but this PRC loses a lot of spell casting ability but doesn't become good in combat. So its just a crappy fighter and a crappy caster. Seems like a strong path to me (/sarc). There may be some class combination that works with this but I haven't found it yet.
Duelist: This is another PrC that was upgraded from 3.5 and is actually decent but very niche. This class allows for unarmored fighters to have great AC and ok damage. It still suffers from terrible Saving throws. You are probably better using base classes to fill this concept. We'll see how the new Swashbuckler class turns out.
Eldritch Knight: The biggest problem with this Prestige class is getting into it. For a few levels you will be a crappy fighter and crappy caster. At very high levels the EK is probably a stronger class than the Magus but you will pull your hair out to get there. Unless it is a high level replacement PC, Magus is usually a better way to go.
Loremaster: The wizard doesn't really get much after level 10 so the temptation is high to leave the class. The Loremaster's prerequisites are probably things you will have anyway so that's not a problem. The biggest weakness of this PrC is that it is pretty weak. Since it keeps full casting I can see why they could not give out any big treats but as it is, why bother taking it?
Mystic Theurg: This is another PrC that looked so awesome when I first started playing. What can be wrong with having both wizard and cleric spells? Well it turns out that there is quite a bit wrong. Lower caster levels, lower level spells, low DCs on your spells. You basically end up with a ton of low level spells. If you want to be a poor healer and a decent buffer than this class is ok but it is a long way from great cosmic power like most full caster classes are. Play a Bard instead.
Pathfinder Chronicler: NPC class. Seriously, what is this? If you are in a campaign that has little to no combat then this class is ok otherwise avoid it.
Shadowdancer: This PrC grants great utility to a sneaky character but its not worth more then a 1 or 2 level dip - 4 at most. The ugly prerequisites limit its use even more. If this PrC was rebuilt as a full base class I could see it being quite useful and popular, now it is just a dip for HiPS.
Other PrC's that deserve mention:
Red Mantis Assassin: Love the imagery of this PrC but i haven't found a good way to build out a PC that uses this Prestige class. I find Ranger works best but RMA casts off Int and the Ranger uses Wis. Maybe the slayer will work well with this? However you roll it, this PrC has serious MAD issues.
Horizon Walker: In the right circumstances (you know you are only going to be playing in one or two environments), this prestige class is immensely powerful. Use Rogue talents to stack up a ton of Favored terrain bonuses and then go to town when you get Terrain Dominance and all creatures native to that terrain become your favored enemies. For an Urban campaign it would not be too hard to get a +10 bonus to hit and damage by level 10 to everything that lives there.
Rage Prophet: These Gish PrC's just don't work. They just dilute the original classes and end up being underwhelming. If you want to cast and smash, go play the new BloodRager instead. They are awesome. Otherwise, stick with either Barbarian or Oracle.
If anyone can point me to a great build that uses any of the PrCs I would be grateful. I like the flavor of many of them but I just can't get them to work in my lab. There are just better ways to do the same thing. To get into many of these PrCs you have to gimp your character for a few levels as you stretch to meet the prerequisites. Often the cool stuff the PrC grants takes a few levels to kick in so there are several levels which can translate into months where you can be unhappy with your PC.