Debts that you can never, ever be completely relieved of because they recur, like apartment rents, utilities payments, and alimony (unless your ex wife gets remarried).

Do they lower your net worth?

Also, on that same logic, does income from a job increase your assets, for accounting purposes?

Rent & utilities are not really debt. You are paying for services and using them every month.

Alimony I would think would lower your net worth.

Your net worth is Assets - Liabilities. Alimony is a form of liability. I have no legal expertise at all, but I think even Alimony has a self life. Even if it's twenty years, the liability would be 20 X Annual Alimony. Utilities and normal bills are not calculated in your net worth.