When entering Roth IRA contributions prior to 2016 to track basis, should I include the amount of a Roth 403(b) rollover that was rolled into my IRA?

[dmertz]

Yes, if that rollover occurred in a year prior to 2016, but only include only the amount distributed from your 403(b) that was your original contribution basis to the Roth 403(b), the amount shown in box 5 of the code H (or perhaps code B) Form 1099-R for the distribution from the Roth 403(b).  Your original contributions to the Roth 403(b) are now contribution basis in your Roth IRAs.