Basically there is no need to index any column. Your Rails application itself won't need them. However, they are (usually) necessary for your database to perform well.
What you usually do in Rails right from the beginning is to index all of your {...}_id columns, because these columns will be used to query associations.
In the end you have to fine-tune database indexes depending on how your application is querying for data and what are key columns. Keep in mind, that adding to many indexes can slow your database down.