If, for whatever reason, you need to be certain you only shoot over 18s then obviously you'll need to make sure they bring appropriate ID for checking before the shoot commences. Make sure it's not their older sister's ID they show you though!
Personally I very rarely feel the need to check ID but obviously it depends what you're shooting and also what you know about the person you intend to shoot with.
I always feel it is wiser to have a parent in attendence when the model is under 18. You will need them anyhow should you require a signed release.
There is no legal requirement but it helps limit risks for very little effort. Anything that could be classed as even risque needs care. I recall there was a big uproar a year ago over a tee shirt featuring a underage model. It was fashion, nothing untoward on show but people felt the pose too sexually provocative.
I always ask for age ID for any level, and for Adult shoots I ask for 2 age ID (government issue) as I believe USA law has something called 2257 Compliance on which the photographer confirms that they have seen two different official age ID documents. This form may or may not be required by US publishers.
This USA bit may well be irrelevant to most on here, but if like me, you sell in the USA then it is relevant.