Annuities have long enjoyed preferential treatment under the tax code - so extensive, that they merit an entire portion of the tax code, IRC Section 72, all to themselves. The favorable rules are generally intended to support the use of annuities as a vehicle for retirement savings and/or retirement income... and as such, the rules generally only apply in situations where annuities are owned directly by individual, living, breathing human beings who may in fact someday retire (known in the tax code as "natural persons").
Accordingly, whether annuities owned by trusts still enjoy tax-deferred growth depends upon the exact details of the trust. The rules do allow that when a trust owns an annuity "as an agent for a natural person" the contract can still keep its tax-deferral treatment, such as when it's owned by a revocable living trust; even if merely all the beneficiaries of the trust are natural persons, such as with a bypass trust for the benefit of a surviving spouse and children, favorable treatment is still available. However, if other beneficiaries are involved - even and including charities - a trust-owned annuity may lose its preferential treatment.
An even more complex point of intersection between annuities and trusts is when annuity contracts are transferred to/from a trust. The problem is a key section of the tax code designed to prevent the unrealized gains of annuities from being shifted to another individual through gifting; as a result, if an individual transfers an annuity "without full and adequate consideration" its gains are immediately recognized. By this rule will not apply to transfers to a revocable living trust, or most types of transfers out of a trust, in the case of some common estate planning techniques - like gifting an annuity to an Intentionally Defective Grantor Trust (IDGT) - the situation remains unclear, and clients and their advisors must be cautious not to accidentally create an unfavorable taxable event!