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.
1) Securing your back-end APIs - If you have a legacy back-end web service that has a basic authentication scheme, you can add some additional security by placing APIM in front, and requiring subscription keys. Leverage your existing firewall to ensure only your APIM instance can communicate with your back-end API, and you've basically added a layer of protection.
2) Lift and shift - there are always going to be clients that don't want to update their clients to use a newer API; in some cases you can make a newer API look like an older one by implementing some complex policies in APIM. You can also do the opposite, making older APIs look new, such as making an XML back-end accept both JSON and XML.
3) Centralizing your APIs - if you've acquired another company and want to make their API set look as if it's a part of the larger whole, APIM is an easy way to provide a consistent front-end interface for developers.
Camel has an easy learning curve. It is fairly well documented and there are about 5-6 books on Camel.
There is a large user group and blogs devoted to all things Camel and the developers of Camel provide quick answers and have also been very quick to patch Camel, when bugs are reported.
Camel integrates well with well known frameworks like Spring, and other middleware products like Apache Karaf and Servicemix.
There are over 150 components for the Camel framework that help integrate with diverse software platforms.
Lack of robustness is a bit of an issue. Several other providers offer more options and capabilities, but then, they are lacking in interface ease.
As with anything Azure, pricing is really hard to stay on top of. I always find that you really don’t know what you’re paying for until you get the bill. Having an excellent Azure Administrator can help resolve that.
Integrating with app services outside of Azure can be a challenge, or at least much more challenging than just using Azure App Services.
If you are looking for a Java-based open source low cost equivalent to webMethods or Azure Logic Apps, Apache Camel is an excellent choice as it is mature and widely deployed, and included in many vendored Java application servers too such as Redhat JBoss EAP. Apache Camel is lacking on the GUI tooling side compared to commercial products such as webMethods or Azure Logic Apps.
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.