My favorite since the DMG came out is Arcane Archer. I like archers, it's one of the first PrCs, and it's powerful. You can shoot arrows around corners - how spiffy is that?
1) It's a high-powered class that boasts high prerequisites. I believe you have to be at least at level 12+ to have a chance at qualifying.
2) Diverse abilities and customization. Lots of options within the class itself lets you choose your powers. This lets high-level mages have a certain area of expertise (Counterspelling, Spell Penetration, etc.), but won't let them master, or even learn, all the possibilities, alleviating the 'cookie cutter' syndrome some prestige classes arguably possess.
3) It fits in almost any campaign. Although it originated in the FRCS, there's nothing really FR specific about it. The class can be used in many settings without change, or be slightly tweaked to add flavor just as easily.
I don't know if they're favourites, but I'm definately getting my milage out of the Gladiator and Fist of Hextor prestige classes in Sword and Fist. I was looking at my local campaign area, and they both just kinda...fit.
For all around favorite and most often taken anymore, Iajutsu Master. I allow Iajutsu (with different names) from several areas of my campagin world, and it's getting very common.
I've used the Ghostwalker. It looked good in the book, but in character, it didn't really seem right. They needed to write a little more about it. All I ended up doing with him was intimidating people constantly.
Guild Wizard (of Waterdeep in Magic of Faerun). Awesome abilities and unlike the majority of overpowered prestige classes, you have to pay XP for this one. Balances it out quite nicely IMO.
I also like the shadow adept, dwarven defender, and divine agent. All very nice classes.