To find the correct match between List I and List II, let us examine each organism listed in List-I and identify its common name or characteristic classification in List-II:

1. A. Rhizopus: Rhizopus is a genus of common saprophytic fungi on plants and specialized parasites on animals. They are found in a wide variety of organic substances, including "mature" fruits and vegetables, jellies, syrups, leather, bread, and peanuts. It is commonly known as bread mould (III).
2. B. Ustilago: Ustilago is a genus of plant parasitic fungi containing species that cause smuts on grasses and crops. Thus, it is commonly referred to as smut fungus (II).
3. C. Puccinia: Puccinia is a genus of fungi. Many species of this genus are plant pathogens and cause rust diseases in many crops. It is commonly known as rust fungus (IV).
4. D. Agaricus: Agaricus is a genus of basidiomycete fungi containing both edible and poisonous species, with over 300 members worldwide. The genus includes the common mushroom, button mushroom, and field mushroom. Hence, it is commonly referred to as mushroom (I).

Matching these pairs, we get:
A - III (Rhizopus - Bread mould)
B - II (Ustilago - Smut fungus)
C - IV (Puccinia - Rust fungus)
D - I (Agaricus - Mushroom)

Therefore, the correct combination is A-III, B-II, C-IV, D-I.