Analog and Digital Output protection?
As mentioned in the comments, it will depend on your system and it's requirements. It's up to you to evaluate your system and its intended use and decide whether or not to include the protection. Here are some examples of things to consider:

Arguments for Protection:


User Error
Users can find wonderful and borderline magical ways to plug things in incorrectly, so adding protections to every electrical connection that the users have access to will make your device more robust. This is especially a concern in consumer electronics which have a lot of users that aren't very technologically sophisticated (or who have children).
ESD
As mentioned in the comments, even properly used devices that aren't always grounded can build up a static charge that can damage your device.
What is the output driving?
If you have an analog output driving an inductive load (such as a simple DC motor or solenoid) you have to protect against inductive kick and Back EMF. If your device is subject to these kinds of events during normal operation, protecting your outputs isn't really an option.
Other
There is always the chance that unexpected conditions may damage a device, even if users are doing the correct thing and ESD isn't a concern. For example, consider an audio mixer (which are always grounded). Even if an expert plugs all the cables in the right way, there may be two worn out cables in a bundle of 30 of them that causes two outputs to be shorted together. If they drive at different voltages, one of those two outputs is going to be very unhappy if it's left unprotected.


I'm going to bundle the arguments against additional protections into one group, because they're pretty much the same as any other electronics projects: increasing the number of components increases design and validation time and complexity, all kinds of costs, and board and packaging size. 

In the end, you have to balance the level of protection required for your product against the various costs associated with implementing those protections.

It's hard to answer your second question without a specific application in mind. For some low voltage analog and digital outputs, a simple diode placed in series with your output may be sufficient. Other situations may require more complex protections like an RC or diode snubber for inductive loads. It just depends on your application.