I thought one of the most important points of creating a living trust was the fact that a trust owns the property (for example) and that I could name a beneficiary of the trust to be my son and then he would get use the house and pass it to whoever he designates as the beneficiary. When an asset gets "pass down" using a trust, there are significant savings on probate taxes and gift taxes. Please correct me if I'm wrong.
Most of my new clients think that too. It is a common belief.
No gift tax savings at all (again, for federal gift taxes. I know some states have gift taxes, but I don't claim to know the ins and outs of all the state laws).... except in certain cases with irrevocable trusts (and a fairly complex and expensive one at that), but a living trust is not an irrevocable trust. During the life of the grantor, all the assets owned by the trust are treated and taxed as if the grantor personally owns them. During the life of the grantor, the trust doesn't even have a separate tax ID number nor file its own tax return unless an third party is trustee, and even then, all of the income flows to the individual's return.
A living trust does help avoid probate, but I don't know of any state that has a probate tax (not saying no states have them, just none that I am aware of). Regardless, the federal gift tax (and estate tax) exemption is currently $5.12 million. If you're in that range you probably want to investigate some of the more complex trusts like zeroed-out GRATS. Plus, there is an annual gift tax exclusion of $13,000 per donee per year (i.e. you can give $13,000 to as many different people as you want each year gift tax free).
The simplest trusts that actually save taxes would be whats known as A/B trusts which go into effect upon death. Trust A (or B depending on the drafter) is a credit shelter which is funded up to the decedent's available estate tax exemption. All remaining assets go into the B trust which is a marital deduction trust. No estate taxes are paid at the death of the first spouse, but the B trust is included in calculating the value of the Spouse's estate upon his/her death.