Generally yes - alimony payments to a former spouse are deductible. However your former spouse must report it as income on his/her tax return. There are a few additional requirements:

1. The alimony must be required under a decree of divirce or legal separation.
2. The alimony must be paid in cash.
3. You and your former spouse must not live in the same household.
4. Your liability to pay alimony must end upon death of your former spouse.
5. If the divorce decree states that alimony is not taxable to your former spouse, then you can not deduct it.

Also in case you're wondering - child support is not deductible.