What are some common examples of SharePoint 2010 services architectures, and what are the advantages of each design?

Single farms with a single service application group are generally the most common, and have the advantages of easy deployment, simple service application allocation, effective resource utilization and cohesive management.

Single farms with multiple service application groups is less common, and have the advantage of potential individual management of service applications as well as allowing data isolation, and while being more complex to deploy and maintain allows targeting of sites to particular service applications.

Enterprise Service Farms is pretty uncommon as it is a complete farm dedicated to Service Applications but promotes autonomous management and high levels of data isolation.

Although there are relevant service architectures  Depending on the environment requirements, a specialized farm can also be used in order to deploy specific services tailored to the organizational requirements which can aid in scaling out and conservation of resources.