An asset you own by yourself and for which you have not designated a beneficiary passes to your heirs according to your will (i.e., according to your own terms and conditions). Assets that you owned by yourself that you then titled in the name of your revocable living trust pass to your heirs according to the terms of the trust agreement. If you die without a will or trust, these assets pass according to the laws of your state of legal residence. If you own real property (and sometimes personal property) in another state, that state's law also may apply to the property and would likely enter ancillary probate after your death. State laws may or may not pass your assets to the heirs you intended.
The main advantage of owning assets by yourself is that you can direct in your will how the assets are to be distributed and/or managed in the future. Leaving assets to someone by beneficiary designation, for example, with no instructions on how they should be managed could lead to problems for the individual(s) inheriting them.
To deal effectively with assets that will not pass to others automatically at your death, it is crucial to have a valid, up-to-date will that is clear and deliberate in communicating your intentions for the distribution of your estate.