You should enter your Roth IRA contributions into TurboTax so that TurboTax can confirm that you have not made an excess contribution and so that TurboTax can track your contribution basis in case you ever take a nonqualified distribution.

(Just make sure that you don't confuse a designated Roth account in a qualified retirement plan like a 401(k) with a Roth IRA.  Assuming that you are not self-employed, contributions to a designated Roth account in a qualified retirement plan are reported in box 12 of your W-2 and are to be entered only in box 12 of TurboTax's W-2 form, nowhere else in TurboTax.)

No you do not have to enter your Roth contributions into TurboTax, however it  will help you keep track of your contributions year to year. 

A Roth IRA contribution does not actually go on a tax return, but you should enter it anyway to:

1) Tell you if your income qualifies you for a contribution and warn you if it does not.
2) Check if your income exceeds the limit to contribute to a Roth.
3) Track your contribution year-to-year if you use TurboTax every year.

4) Add the Retirement Savers Credit if you qualify.

5) Track of your contributions through the years, and if you overpaid, or had pay back anything, it will keep track of it for you.

To enter Roth IRA contributions in TurboTax:

1. Federal Taxes,
2. Deductions & Credits,
3. Retirement & Investments,
4. Traditional & Roth IRA contribution.