It is important to make sure that the agency you use is licensed, preferably in your state. Some states' laws require that most potential adoptive parents complete a pre-placement home study with an agency licensed in their state. If the agency isn't licensed, your home study may not be accepted by the court.
What types of placements does the agency handle?
There are many types of adoptive placements - domestic infant adoption, international adoption, adoption from foster care, special needs adoption, interstate placements. Some agencies offer placements in only one area (for example, domestic infant adoption) while others offer a variety of placements. If you are focused on a particular type of adoption or if you want to have multiple options, knowing what type of placements an agency offers can help narrow your choices down.
Does the agency focus on a special population?
Some agencies may focus on placement of children in families with a particular religious affiliation. Others may work particularly with minority or special needs children. Many (if not most) place children of varied backgrounds in families of varied backgrounds! Knowing whether an agency serves only a limited population can inform your choice of the best agency for you.
What pre- and post-adoption services are available?
More and more agencies offer pre-adoption counseling to (or even require it of) potential adoptive parents. Post-adoption services such as support groups, resource libraries, referrals to community resources, respite care, and post-adoption counseling can be invaluable to adoptive families. But, just because an agency doesn't directly offer such services shouldn't necessarily rule them out; if an agency doesn't directly offer a lot of pre- or post-adoption resources, find out about their referral network.
What services does the agency provide to birth parents?
It is important to know whether multiple options (especially the ability to parent and resources available to make that work) are discussed with birth parents (especially birth mothers). It is also important to know whether birth parents receive counseling. A fully informed and counseled birth mother makes a fully informed and counseled choice and is less likely to change her mind. In my opinion, an agency that has a low placement rate (i.e., most of the women it counsels choose to parent) is not a cause for concern. What should concern adoptive parents is the fail rate (i.e., the number of women who change their mind after a match is made and especially after a placement is made). You will also want to know how the agency makes sure that birth mothers get adequate prenatal care (or if they do make sure).
What level of openness can you expect in the typical adoptive placement with the agency?
Fully closed domestic adoptions are rare nowadays, but the level of openness varies. At one end of the spectrum, an adoption may be open only to the extent that non-identifying medical and genetic information is shared. At the other end, the birth parent(s) and adoptive parent(s) may share an ongoing relationship with lots of contact. In my experience, it is common for the adoptive family to be expected to share several updates with the birth mother (letters, photos, etc.) in the first year and annual updates after that, with additional contact left to the discretion of the adoptive parent(s) and the mutual agreement of the adoptive parent(s) and birth parent(s). If you are considering adoption, you should consider your comfort level with ongoing contact and the maximum level of contact you'd view as comfortable.
In international adoptions, the level of information available varies widely as does how "open" an adoption may be.
What does it cost?
I intentionally put this question last because, in my opinion, cost should not be the first criterion driving your decision. It is important to find an agency with which you feel comfortable because your relationship with the agency may drive the adoption process. That said, cost is not unimportant. It is most important to understand what is covered and what is not. Is the fee all-inclusive? Will you be expected to pay additional fees if the birth mother needs financial assistance? If she doesn't have health insurance? If your home study and background check becomes "stale," what is the cost to update? Is any portion of the fee refundable if no match is made within a particular period of time? If the birth mother changes her mind following placement?
Additional resources provided by the author
There are numerous online resources for potential adoptive parents. I particularly like the Dave Thomas Foundation, the Evan B. Donaldson Adoption Institute, the U.S. Department of State's website on intercountry adoption, the North American Council on Adoptable Children, and the Child Welfare Information Gateway's foster care and adoption directory.