The common nitrogen-fixer in paddy fields is azospirillum. It is a gram-negative, non-fermentative, microaerophilic, nitrogen-fixing bacteria. It also has the capacity to synthesize phytohormones specially indole-3-acetic acid and gibberellins and helps in promoting root proliferation.

The common nitrogen fixer in paddy fields is Azospirillum.

Explanation:
Paddy fields are flooded agricultural fields that are specifically used for growing rice. These fields are unique because they are continuously submerged in water, creating an anaerobic environment. In such conditions, the availability of oxygen is limited, which affects the nitrogen cycle in the soil.

Nitrogen is an essential nutrient for plant growth, and it is often a limiting factor in agricultural systems. While atmospheric nitrogen is abundant, plants cannot directly utilize it in its gaseous form. Therefore, certain microorganisms called nitrogen fixers play a crucial role in converting atmospheric nitrogen into a form that plants can use.

Azospirillum is a well-known nitrogen-fixing bacterium that is commonly found in paddy fields. It is a free-living bacterium that forms a mutualistic relationship with rice plants. Azospirillum lives in the rhizosphere, which is the region of soil surrounding the roots of plants.

Benefits of Azospirillum in paddy fields:
- Azospirillum has the ability to fix atmospheric nitrogen into ammonia, a form that plants can assimilate. This helps in increasing the nitrogen availability in the soil and promotes the growth of rice plants.
- It also produces growth-promoting substances like auxins and cytokinins, which stimulate root development and overall plant growth.
- Azospirillum can solubilize phosphorus, making it more accessible to plants.
- It enhances the uptake of other nutrients from the soil, thereby improving the nutrient status of the rice plants.

Other options:
- Rhizobium: Rhizobium is a nitrogen-fixing bacterium that forms a symbiotic relationship with leguminous plants. It is not commonly found in paddy fields.
- Oscillatoria: Oscillatoria is a filamentous cyanobacterium that can fix atmospheric nitrogen. However, it is more commonly found in freshwater bodies like ponds and lakes, rather than paddy fields.
- Frankia: Frankia is a nitrogen-fixing actinobacterium that forms a symbiotic relationship with certain woody plants like alder and casuarina. It is not commonly found in paddy fields.

Therefore, the correct answer is option B) Azospirillum.