This is not a free service and does not have an option for a free plan. It only has a free trial.
They don't list pricing on the website. When you create an account it starts a 30-day Pro trial, after which, you have to select a Pro plan.
Current rates as of 2015-06-25:
$8/mo, or $80/year (USD)

Here is the info from their website:

Free trials
If you sign up for a free 30-day trial of Hours Pro on the web, you will get all of the Pro features on both the iPhone and on the web without restriction for 30 days. When you come to the end of your trial, you can either pay to continue the Pro features or continue using the iPhone app without web access and Pro features, but without losing any of your own time tracking data."

While you are on the free trial, you can also create teams and add team members to your teams at no charge. At the end of your trial, you can begin paying the monthly subscription for your team members or discontinue using teams. If you subscribe, you can first change the number of team members if you wish. If you do not subscribe, your team members' data will still reside on their individual accounts, and the team can even be put together again if you later decide to pay for the team.