There are 2 types of “special,” non-magical arrows in the core rules: silver arrows and adamantine arrows. These arrows overcome the damage resistance and/or damage immunity of the target. (Arrows aren’t special here, the above is true for daggers, etc.)
There’s no list, exactly, but here is where you’d find them:
Silvered weapons are described p. 148 of the Players Handbook. Silvered weapons are expensive but generally available.
Adamantine isn’t mentioned in the Players Handbook, and there’s no “set price” for them. Although Adamantine Armor is a magic item, the (DM Guide, p 150) the Monster Manual mentions “nonmagical weapons that aren’t adamantine” (MM, p. 140, etc.) in several places. It’s left to the DM as to how these might be acquired.
There are no other special arrows, like whistling arrows, etc., specified in the core rules. (But the rules don’t exclude them either, so as ever, talk to your DM.)
Update: Xanathar’s Guide to Everything, published since this answer was edited, lists a price for adamantine weapons as 500GP + the value of the normal item.
The adamantine version of a melee weapon, or of ten pieces of ammunition costs, 500 gp more than the normal version, whether the weapon or ammunition is made of the metal or coated with it.(page 75)