Using Android without Google account I don't like the idea that my personal information are gathered and by some company that make profit out of processing and selling it (or even when it has a possibility to do so). And yes, that's the reason I don't use Facebook and gmail (after reading their TOC).

I wonder if it's possible to use the Android smartphone without Google account at all in a long time?

So far I know that:


I don't use gmail/google+/chrome, so I don't bother about it.
I cannot download application from Google Play without Google account, but I can download most of them as .apk and install manually.


Did I miss something? Or it's possible to live with Android without Google account?

p.s. Does Google still collect any data about me, even when I just use Android, without Google account and without gmail/google+/youtube?
Of course you can, in fact, the only reason a lot of people connect their Google account is to use play store and get apps easily. 

I suggest you to install F-Droid: it is the best source for open source Android apps, where you can find a "copy" of all g-apps. 

For the last part, technically, if you answered No to all google's attempt to get you accept their therms and conditions, they can't. But keep in mind that a lot of applications are based on Google API, so, they would use things like Google Play Services to get some jobs done. (I'm not sure, but I believe they pass all information directly to the app without saving anything on their databases about you if you did not accept TOC)

If you really want to avoid Google, I suggest the use of a custom ROM