I have an application that uses SQL Server where I plan on deploying four instances to four different third-party dedicated hosting providers. The databases will replicate between each other. So, does each SQL Server reside in its own AD domain or should there be one AD domain regardless of location?
What are the pros and cons of each?
SQL Server Replication uses local accounts rather than domain user accounts, so multiple domains really shouldn't pose a problem with respect to replication. Replication is designed to handle distributed clients and disparate environments relatively easily. I'm not a Windows domain genius, but I imagine that the work required to set up four member servers in the same domain across four different hosting providers will outweigh any managemability gain that you may stand to achieve.
I agree with Aaron. This is not a scenario for using AD infrastructure. I would go for standalone servers and using SQL authentication for connectivity between them.