Quick answer: a special spousal marital election, military death benefits, certain retirement accounts, and charitable transfers all escape this tax, on top of the class-based rates in Rates & Who Pays.
A spousal election that predates federal portability
Military death benefits are exempt
Benefits from the federal government arising out of military service are specifically exempt from Kentucky inheritance tax under KRS 140.015, separate from and in addition to whatever class exemption the beneficiary might otherwise have.
Certain retirement accounts get their own exemption
Annuities or other payments under employees' trusts, retirement annuities, and individual retirement bonds, accounts, and annuities have a dedicated exemption under KRS 140.063 — worth checking carefully against the specific account type involved, since not every retirement vehicle is treated identically.
Charitable, educational, and religious transfers are exempt
Transfers to educational, religious, or charitable institutions, societies, or associations, and to cities, towns, or public institutions, are exempt under KRS 140.060 — separate from Class C, which covers non-qualifying institutions and organizations that don't meet this exemption's requirements.
A local probate attorney can review your estate — many offer a free consultation.
Life insurance proceeds also receive specific treatment under KRS 140.030 — have a Kentucky attorney confirm exactly how a given policy's proceeds are classified for your situation.