To determine which statements regarding ocean currents are correct, we need to evaluate each statement individually and understand the causes and factors related to ocean currents.

1. Statement 1: Difference in water density is the main cause for the formation of ocean currents.

This statement is correct. One of the primary drivers of ocean currents, particularly deep ocean currents, is the difference in water density. These density differences are caused by variations in temperature and salinity, leading to what is known as thermohaline circulation.

1. Statement 2: Density of water depends on temperature, salinity, and pressure.

This statement is also correct. The density of seawater is influenced by its temperature, salinity, and to a lesser extent, pressure. Cold, salty water is denser than warm, fresh water, causing it to sink and create deep ocean currents.

1. Statement 3: As a rule, ocean waters move from areas of higher density to areas of lower density as a current.

This statement is incorrect. Instead, ocean waters typically move from areas of lower density to areas of higher density. The denser water, being heavier, tends to sink and is replaced by lighter, less dense water, forming a circulation pattern.

After analyzing all the statements, we can conclude:

• Statements 1 and 2 are correct.
• Statement 3 is incorrect.

Therefore, the correct answer is \(1 \text{ and } 2 \text{ only}\).