Can I avoid the gift tax by gifting or leaving everything to my spouse?

Yes, transfers between spouses are 100% deductible for Gift Tax purposes. This is known as the "unlimited Gift Tax marital deduction". However, the value of the gift, whether it was for a future or present interest, is included in the giver’s gross estate on death in order for the deduction to apply. If the gross estate does not include the transfers to the spouse, no marital deduction applies.

This gift exclusion only applies to gifts to a U.S. citizen spouse.