Code re-use -- if you code drivers/protocol-handlers using an RTOS API they may plug into future projects easier
Debugging -- some IDEs (such as IAR Embedded Workbench) have plugins that show nice live data about your running process such as task CPU utilization and stack utilization
Usually you want to use an RTOS if you have any real-time constraints. If you don’t have real-time constraints, a regular OS might suffice. RTOS’s/OS’s provide a run-time infrastructure like message queues and tasking. If you are just looking for code that can reduce complexity, provide low level support and help with testing, some of the following libraries might do:
There are many many reasons you might want to use an RTOS. They are varied & the degree to which they apply to your situation is hard to say. (Note: I tend to think this way: RTOS implies hard real time which implies preemptive kernel...)
Rate Monotonic Analysis (RMA) - if you want to use Rate Monotonic Analysis to ensure your timing deadlines will be met, you must use a pre-emptive scheduler
Meet real-time deadlines - even without using RMA, with a priority-based pre-emptive RTOS, your scheduler can help ensure deadlines are met. Paradoxically, an RTOS will typically increase interrupt latency due to critical sections in the kernel where interrupts are usually masked
Manage complexity -- definitely, an RTOS (or most OS flavors) can help with this. By allowing the project to be decomposed into independent threads or processes, and using OS services such as message queues, mutexes, semaphores, event flags, etc. to communicate & synchronize, your project (in my experience & opinion) becomes more manageable. I tend to work on larger projects, where most people understand the concept of protecting shared resources, so a lot of the rookie mistakes don't happen. But beware, once you go to a multi-threaded approach, things can become more complex until you wrap your head around the issues.
Use of 3rd-party packages - many RTOSs offer other software components, such as protocol stacks, file systems, device drivers, GUI packages, bootloaders, and other middleware that help you build an application faster by becoming almost more of an "integrator" than a DIY shop.
Testing - yes, definitely, you can think of each thread of control as a testable component with a well-defined interface, especially if a consistent approach is used (such as always blocking in a single place on a message queue). Of course, this is not a substitute for unit, integration, system, etc. testing.
Robustness / fault tolerance - an RTOS may also provide support for the processor's MMU (in your PIC case, I don't think that applies). This allows each thread (or process) to run in its own protected space; threads / processes cannot "dip into" each others' memory and stomp on it. Even device regions (MMIO) might be off limits to some (or all) threads. Strictly speaking, you don't need an RTOS to exploit a processor's MMU (or MPU), but the 2 work very well hand-in-hand.
Generally, when I can develop with an RTOS (or some type of preemptive multi-tasker), the result tends to be cleaner, more modular, more well-behaved and more maintainable. When I have the option, I use one.
Be aware that multi-threaded development has a bit of a learning curve. If you're new to RTOS/multithreaded development, you might be interested in some articles on Choosing an RTOS, The Perils of Preemption and An Introduction to Preemptive Multitasking.
Lastly, even though you didn't ask for recommendations... In addition to the many numerous commercial RTOSs, there are free offerings (FreeRTOS being one of the most popular), and the Quantum Platform is an event-driven framework based on the concept of active objects which includes a preemptive kernel. There are plenty of choices, but I've found that having the source code (even if the RTOS isn't free) is advantageous, esp. when debugging.
RTOS, first and foremost permits you to organize your parallel flows into the set of tasks with well-defined synchronization between them.
IMO, the non-RTOS design is suitable only for the single-flow architecture where all your program is one big endless loop. If you need the multi-flow - a number of tasks, running in parallel - you're better with RTOS. Without RTOS you'll be forced to implement this functionality in-house, re-inventing the wheel.
Additional to the points mentioned before, using an RTOS may also be useful if you need support for
Most RTOSes provide these features or are expandable to support them