The company (crew scheduling) can extend you (on paper) up to 24 hours on a domestic trip, and 48 hours on an international trip. Of course if the plane is hard broke, or some other calamity, you could be on the road longer. Your trip value would be increased (in most cases).

Additionally (if you get back to domicile more than 4 hours late), you are paid "late arrival pay" which is normally 150% (and can hit 250%). That pay is calculated as a new, independent "trip" that starts when you were originally supposed to get home. It can be a lot of $$$.

The rules for reserves are similar but not quite as lucrative.

Also, you can opt for compensatory days off in lieu of late arrival pay, but there are restrictions about that and most pilots just take the extra $$$.

You cannot refuse an extension unless you have military duty or something similar, or vacation.

Depends on the fleet, but on the international side, it occurs somewhat frequently (Personally, I see it every 1-3 months)