Can I collect on a life insurance policy that I have on my ex-spouse in the event of their death?

In order to own and pay for life insurance you must have what is known as an "insurable interest." Insurable Interest has been defined as the requisite connection between the owner/payor and the person whose life is insured.  This requirement usually demonstrates that the purchaser will actually suffer some kind of loss if the insured dies; for example, as in the case of a financially dependent spouse or former spouse and children in the life of a former spouse. 

If you receive alimony or if you are receiving child support then you have an insurable interest;  otherwise, you probably do not.  Possibly your divorce decree addresses this issue?

To be certain of your rights under state law, you should discuss this matter with a local attorney or at least contact the applicable Department of Insurance.