Here are my two cents. You may or may not trade based on economic data, but you need to be aware of them, especially if you intend on having a position when the data is released. This is especially true in case of commodities and currencies, which tend to be quite sensitive to economic releases. Having an intraday/short-term position and not being aware that an important data would be coming up could lead to trading losses (if you fortunate enough, can lead to gains as well).
As an example, the US employment data is released on the first Friday of every month. This is one of the most widely sought economic data as it tells about the health of the labor sector of the world's largest economy and has a bearing on the Federal Reserve's monetary policy as well. Hence, commodities tend to be quite sensitive to this data. This is especially true in case of precious metals. If you see the historical charts of gold and silver, you will see that they tend to be quite volatile as the data is released. Hence, if you are trading gold and silver, you need to be aware of this. In a similar fashion, there are many other economic releases that impact movements in commodities and currencies. If you trade these assets, you need to be aware of when these data come out.
In case of equities, domestic inflation, trade balance, industrial production, GDP etc. are some of the data that impact the Indian markets. However, the impact tends to be less severe, unless there is a significant deviation from forecast.
Another thing, not all data impact each instrument in the same way. You need to be aware of which data will impact which instrument and the sort of impact. For instance, the US GDP is likely to have an impact on gold but is unlikely to have much of an impact on, say, wheat or Reliance Industries.