If the subject is merely a subject within a larger composition, no. No more than I would ask anyone if they mind if I look at them with my eyes. That is what being in 'public' is all about.
If, however, I want a composition where the subject is the centerpiece of the composition, then I raise my camera, make eye contact with him/her, and mouth "ok?" I've never been turned down doing this. I don't really need to do it, but it is just a matter of courtesy in that specific situation.
Legally, anyone in public is subject to photography, so long as that photo is not used in a commercial/advertising manner without waiver. Documentary use is always permitted (at least in the US).