Were either of these an IRA or 403(b) annuity?

If not in a retirement account, and as you took possession of the funds from the first annuity (you stated you received a check), then the cash out of the first annuity is taxable.  Wait for the 1099R for how much is taxable.

Now if you did not take possession of the funds, but rolled one annuity into a second annuity, then it was a legal exchange and likely not taxable.

Does this need listed on my 2016 tax return?

A Section 1035 exchange will be reported on Form 1099-R with code 6.  Wait for the Form 1099-R.  Any Form 1099-R that you receive regarding this must be reported on your tax return.

Questionable if this is a valid 1035 exchange.  Not valid if OP took possession of money at any time.

I never took possession of the funds, the check was endorsed directly over to the new annuity company.

If the check was made out to you personally, the transaction does not qualify as a 1035 exchange and any amount distributed in excess of the amount of any after-tax premiums in the old annuity not previously distributed would be taxable.  If the check was made out to the new annuity company for your benefit, it probably does qualify as a 1035 exchange.