Rebuilding Index in SQL Server 2014 During index rebuilds through Maintenance Task in SQL Server 2014, do we need to apply Keep Index Online while re-indexing option in the Maintenance Wizard ?
Only you can answer that question.

The option will make the index rebuild operation an online operation. See Perform Index Operations Online. There are certain limitations and restrictions, I recommend you read the link above and Guidelines for Online Index Operations as well. To call out a few issues, online operations have licensing edition restrictions, they consume more disk space, they take longer, and they pin the log from shrinking. However, they do allow for the application to continue to function online while the rebuild is ongoing. So, as you see, only you can answer what you need. Take the time, study, and make an educated decision.

Also, is very unlikely that you need to rebuild indexes for maintenance. Have a look at SQL Server Index and Statistics Maintenance.