As a DM - Depending on the age category (I allow middle-aged and older PCs, though they are much less common at 1st lvl) and the race, the player chooses an appropriate age.
As a player - depends purely on the character concept.
My youngest PC was an elf around the equivalent of 15. My oldest is my current character, a human who started at age 27. His birthday is coming up, though (yeah, we've got birthdays for our characters).
18-25 is "Journeyman" age, which is where I've started my games so far. "Apprentice" age might be interesting for a lower-power game, but they're not going to be doing much slaying.
Since we rarely start characters at lower than level 5, we rarely end up with characters younger than 25 years old. As it stands now, all my characters are in the 25-30 range. I've had 1 old character, that started old, to reap the benefits of improved mental stats.
PCs start at an age picked or rolled according to player preference, but must be at least the minimum age to for the respective character class according to charts in the PHB, Races of Faerun, or other source.