If someone owes me money, can I take out a life insurance policy on them without their knowledge and be listed as the beneficiary?

In a word: no. It is against the law to insure another person without their consent. You could ask the debtor to take out a policy naming you, though it's unlikely they would.

Your recourse is to sue the debtor for the money. You should retain a lawyer to help you, though you could legally do it yourself. Assuming the debt is valid, you can prove it, and you win, if the debtor still doesn't pay, at that pont you'd have several different options to collect, including garnishing wages or a bank account, putting a lien on real estate, possibly causing some of the debtor's belongings to be sold for your benefit, etc. That's the way to collect--not with a life insurance policy.