MySQL replication as both master and slave (replication loop?)
Terminology

What you're describing is a common set up that may be variously described as master-master replication, dual-master, active-active, bidirectional, or a few other terms.

Good reasons not to do it

The team who wrote High Performance MySQL offer this pithy summary of master-master replication - specifically, "active-active" replication:


  In general, allowing writes on both servers causes way more trouble than it’s worth.


Baron Schwartz, one of the authors, offers a slightly more blunt opinion on his blog.


  Save yourself grief, work, and money. Never write to both masters.


There are many things that can go wrong if both servers are updating data at the same time, including (but by no means limited to):


If something goes wrong with replication - even a temporary network glitch, you'll likely end up with a split brain and it may be impossible to determine which data is "correct"
If AUTO_INCREMENT MySQL settings are wrong, it's easy for data collision to take place
Row locking no longer offers any protection - data can be manipulated on one master even while a transaction has it locked on another


Good reasons to do it - carefully

The most common reason for master-master replication is to so that you can very quickly switch the "current" master if something goes wrong with one of your servers.

The common way to implement this is to set up a barrier that ensures that only one of your servers is every written to by your application servers. This is usually a hardware load balancer, or software load balancer like HAProxy.

The authors of High Performance MySQL (mentioned above) describe this as "active-passive" master-master replication.

As long as the barrier is robust, you are fairly well protected from all of the issues described above. This may be supported by setting read_only on the "passive" server for an extra layer of protection.

A well-built master-master setup can offer you some amazing flexibility - you can do some really complex table or server maintenance on your passive server, wait for replication to catch up, then migrate your load balancer over to point at your shiny, reconfigured environment with almost no service downtime. This sort of thing does need to be planned carefully, though, and a lot can go wrong.