Online Express supports free events and free price types.
You can hide the price column completely if all of the price types for an event are free. Obviously if there is one or more paid price type the price column must be displayed. In the case where there are a mix of free & prices, you can customize the language of how a free price is displayed. For example, instead of displaying £0.00, you can display "Free" or "Complimentary".
Finally, if someone is registering for a completely free event, they will not be prompted for any payment information. This happens automatically and you do not have to set up anything special for it to work.