Strictly personal acts, which the law reserves for the person concerned. The most common one is the will: nobody can make it on your behalf, not even with a power of attorney. Taking the oath or promise for Spanish nationality cannot be delegated either.
Some procedures also require you to be there in person even though they are not strictly personal, such as having your fingerprints taken for the TIE. The procedures people living abroad usually have pending (property sales, inheritances, the NIE, the tax office, banks, lawsuits) can all be done through a representative.