Private adoption agencies are state-licensed and some are for- and non-profit businesses. Although licensed under the same requirements, adoption agencies can be radically different from one another. Some may have rules against adopting out to single parents and others may not adopt to gays or people of a certain age. This doesn't make an agency worse than another, and it's not illegal for private agencies to be picky about who they place children with.
What it means to know of the best adoption agencies, depends on what you value. The best adoption agencies are those that can meet a couple's needs within their budget. The best adoption agencies are also those that protect the birth mother by respecting her rights.
To find the best adoption agencies, you may want to ask around for referrals. Health care providers, who may also be referring adoption agencies to birth mothers, may have a list they can provide you. A case worker performing a home study may be able to point you toward an agency that you'd work well with. An adoption attorneys may know of good agencies, having dealt with them on a regular basis. And, there are always adoption forums and Better Business Bureau ratings to help inform your decision.
Some experts suggest that prospective adoptive parents work with multiple agencies to increase their chance of placement in a timely manner.
If you're looking to adopt an older child, then you'll be working with a public adoption agency that's run by the state.