Executors are commonly compensated for their services. Someone who stands to inherit under the terms of your will may be more inclined to waive payment for acting as executor. Since the estate pays the fee, it is probably going to be deducted from his bequest to some extent anyway. Avoiding payment of the executor eliminates one step of the probate process and might cause it to be settled sooner. If you trust your executor a great deal -- and your other beneficiaries do, as well -- you may feel comfortable waiving the requirement that he post bond, which most state laws will demand unless you expressly waive the responsibility in your will.
Since the job of an executor is to pay your debts and taxes, then distribute the balance of your estate to the beneficiaries, it creates a conflict of interest for a beneficiary to disburse funds from the estate that would otherwise go to him if those debts were declined for payment. Small estates that run the risk of insolvency -- having more debts than assets -- can put the executor in a bad position if he is also a beneficiary. There might be limited funds to disburse at the end of probate, making it impossible for all beneficiaries to receive the full amount they were supposed to receive under the will. In this case, your executor would have to decide how much to give each beneficiary, including himself.
If you name a beneficiary as your executor, consider also naming a co-executor to provide a second opinion if any conflicts of interest arise. At least name an alternate executor, because if your other beneficiaries petition the court to remove your beneficiary/executor because they don’t think she is acting fairly, you have a backup in place to take over.
Actions taken by an executor during the probate of an estate are usually monitored by the court, so the opportunity for any actual wrongdoing by an executor who is also a beneficiary is limited. If your estate is small and all your beneficiaries are next-of-kin, the choice of an executor may not be as critical. The position may not require a great deal of financial expertise, so paying executor fees to a professional would not be worthwhile. Also, be honest with yourself as to how well all your beneficiaries get along. Naming one of them as executor could either facilitate the probate process or cause unnecessary complications.