Message brokering across different systems, with transactionality and the ability to have fine tuned control over what happens using Java (or other languages), instead of a heavy, proprietary languages. One situation that it doesn't fit very well (as far as I have experienced) is when your workflow requires significant data mapping. While possible when using Java tooling, some other visual data mapping tools in other integration frameworks are easier to work with.
Multiple systems to interface for a task in the company (example: to sell an item your POS must communicate with the inventory software, then to accounting, then to service, etc).
When a task must bring information from several external services.
When you have to deal with multiple APIs.
Not recommended for:
Data transformation (although Talend has a software for that that works with Talend ESB)
Some of the documentation is a little sparse. In particular, its TCP-based routes use an underlying Netty server, and the interactions between Netty's decoder capabilities and Apache Camel's routing/handler capabilities can be a little muddy at times. In general it is clear which routes and endpoints are the more frequently used and which haven't been given as much attention.
Apache Camel has been the integration framework of choice, but I was not the person to make the decision to use it. Compared to other competing products like Tibco Business Works, etc., it is free and open source and its licensing policy is acceptable to the management of Cox.
Very fast time to market in that so many components are available to use immediately.
Error handling mechanisms and patterns of practice are robust and easy to use which in turn has made our application more robust from the start, so fewer bugs.
However, testing and debugging routes is more challenging than working is standard Java so that takes more time (less time than writing the components from scratch).
Most people don't know Camel coming in and many junior developers find it overwhelming and are not enthusiastic to learn it. So finding people that want to develop/maintain it is a challenge.