In my home campaign (average party level: 7, two 8th level characters), I currently have 5 players. Only one is working towards a prestige class. At least 4 NPCs have taken prestige classes though. . . .
PCs
Rgr/Ftr/Rog (dual shortsword wielder)
Bbn
Rog/Sor (working towards Arcane Trickster)
Clr
Rgr
NPCs
Ftr/Necromancer/Acolyte of the Twisting Serpent (thanks Tuerny)
Ftr/Ravager
Rgr/Pal/Hunter of the Dead
Clr/Wiz/True Necromancer
In the Return to the Temple of Elemental Evil campaign I play (current party level: 6, with two 7th level characters), we have one PC aiming for a prestige class, IIRC:
Ftr/Master of Chains
half dragon Bbn
Ftr
Sor
Rgr/Drd
Clr (7th level archery specialist--no prestige class plans)
In Living Greyhawk, among the people I regularly play with:
Ftr 2/Wiz 5 (aiming for spellsword and Sacred Exorcist)
Clr 2 (plans on staying a single-classed cleric)
Pal 5 (no current plans to gain a prestige class that I'm aware of)
Bbn 1/Clr 1 (no current plans for a prestige class)
Rog 1/Ftr 1/Brd 4 (constantly changing plans for a half dozen prestige classes--mindbender, spymaster, virtuouso)
Clr 7 (no plans or skill points for prestige classes)
Ftr 1 (plans to go Cavalier, IIRC)
I suspect that a bit more than half of the characters are currently aiming at prestige classes (this is not really a representative sample). This is certainly true of my characters:
Ftr 2/Wiz 5 (plans for Sacred Exorcist and Spellsword)-Living Greyhawk
Clr 2 (none)-Living Greyhawk
Bbn 2/Ftr 1 (possibly Devoted Defender--definitely no other plans)-Living Arcanis
Rgr 1 (no prestige class plans)-Living Kalamar
Wiz 5/Wizard of High Sorcery 1-Homebrew Dragonlance game
Sor 6/Candlecaster 4/Elemental Savant 4-Homebrew game
Clr 7 (none)-RttToEE
Pal 6 (none)-Homebrew Sea of Fallen Stars game
Rgr 1/Clr 3 (planning for Templar)-Homebrew Greyhawk game
Ftr 3/Rog 3 (planning for custom prestige class: Sons of Gryphos)-Homebrew game
About 2/3 of my characters are running after prestige classes. I think that may be typical.
As a DM, I enjoy the flexibility to create NPCs with new and special abilities that prestige classes afford me. As a player, they offer quite a few nifty abilities and make some character concepts possbile that the core rules do not support well.