If you are interested in third-party services that allow people to download any application from Google Play through another service, I would not worry about it, because it is difficult to say how authentic / official these services are. They may offer versions of your application with malware / spyware / adware and those added for everyone you know. I would just assume that your users have Google Play (if you only purposefully offer it on Google Play), and don't worry about it, or claim that Google Play is a requirement for your application.
If this is not what you requested, here is the answer to another interpretation of your question:
Google Play can only be installed legally by the manufacturer (although it can be installed illegally by someone, the last time I checked).
There are many Android devices that do not ship with Google Play installed, but must have the popular, more expensive devices that many people use. Some of the less expensive and / or lesser-known ones will also have it (but do not count on it and do not expect it to be installed legally where it exists in 100% of cases). I think Google has a list of authorized devices, if you're really curious about which ones are legally. I am not sure if it is 100% updated.
Something you really need to know is that Amazon Kindle Fire devices do not have Google Play, but they are still technically Android devices capable of running Android applications (although the OS is adapted to be slightly different from standard Android). Instead, they use the Amazon App Store. It can be easily installed on other Android devices, regardless of whether they have Google Play (so this is not just a Kindle Fire application, but it is a useful store for everyone who does not have Google Play).
I personally recommend developing an application to work with both Google Play and the Amazon app store to allow anyone to use your application or at least offer apk regardless of the AppStore on your personal website (regardless of whether to sell give it there for free, it doesn’t matter, people need a way to access it if they don’t have Google Play - if it works without Google Play, anyway).
I personally found that most of the Android devices I wanted to buy were not installed on Google Play. I did not look at the high-end devices, though (for example, Nexus 7, Galaxy Table or something else).
It seems that more phones are probably pre-installed than tablets. Tracfones etc. They often have it (although I do not recommend them if you are looking for an Android device with Google Play, even if it can have it).
You can design your application to require Google Play (many applications), and rely on other Google applications, but it blocks you in the Google environment and excludes people outside it. You like that it is enough for your purposes or not, it is up to you.
If you do not have any alternative applications for Google applications that you want to use (Gmaps, etc.), you can also support Google Play requirements (usually you will not find regular Google applications in other applications). If you have alternatives available in the Amazon app store (or other similar ones), you can try them out and see if they work. So yes, make sure that all the dependencies of your application are available to the user. They cannot automatically download material that is not in their application store, and they cannot use Google Play (and therefore official Google applications) if they do not have it.
But then again, I don't want it to sound like you shouldn't use the Google Play and Google apps. They may or may not be the only ones currently available that are suitable for your purposes. Of course, you will have to explore other applications. If you do not need, you can check again and again in the future, for new applications that meet your goals (maybe once a year or two).