I have several phones, I run Android (mainly Cyanogenmod) and SailfishOS, and I don't have any Google Apps on my phones. It doesn't stop you from using the apps that are only made available on the PlayStore, because you can easily sideload them with things like apkdownloader. If you use Cyanogenmod 11, the privacy sensitive access those apps require can be blocked by Cyanogenmod's app permission system, and by the built-in firewall. I have all the apps I want on my phones, and don't install apps that are crazily criminal when it comes to privacy rights violations, like Skype.
However, I also have several tablets. One of my main tablets is the Nexus 7 2013, which runs on the stock Google and isn't even rooted. It is registered to a bogus Google account that means nothing, and I use K9Mail for the real email accounts, which are not system-wide, and configured that Google doesn't spy on them. I occasionally sideload apps, but mainly get all my software from f-droid.org, which is all open source and very limited in privacy invasion and system access. I don't use the GPS function on it, and only use it from behind a strict Linux netfilter (it's WiFi only, so that solves a lot of privacy issues) that runs on a portable storage server/hotspot on which I store my documents and work, so that I can access it everywhere. It doesn't use any Google cloud services, it's a part of my own private cloud solutions, both for home and office use. My own cloud runs from my own servers, which are all hardened linux boxes that are entirely virtualized with NIC passthrough setups and dedicated NICs.
I wanted to keep the stock Google Android on the Nexus 7 because of the early updates, but I might just install Cyanogenmod on it once Cyanogenmod catches up a little bit more in the nightlies. On my phones, the Android ones of which run CM 11, Dalvik has been replaced by ART and it works great. With the 4.4.3 update from Google for the Nexus 7, Dalvik is still the default HAL and you can't change it to ART in the settings, so I'm pretty pissed off at Google for that. The net result is that I have cheap Chinese 80 USD tablets that run faster than the Nexus 7 2013 and with more recent Android software (but not such a nice screen as the Nexus 7). The problem is that Cyanogenmod hasn't quite caught up yet for bringing fully functional CM 11 to the Nexus 7 2013. The moment that happens, I'll reflash the Nexus 7 and dump the GApps from it, but I use the device a lot, it's become my main computing device in many aspects (I'm a small mobile computing devices fanatic, everything from calculators to PDA's etc... have always used them, love them to bits, love them more than PC's), so I want to be sure that everything will work, and I'm not convinced by the CM nightlies for the flo at this point in time.
Google is generally very bad news when it comes to respect for elemental human rights. GApps is the best example of that. Do you know that the newest Google keyboard has a built-in keylogger? According to Google, this was added of course because they want to improve the user experience... yeah... whatever... on a phone, that is always connected and locatable, and on which the application processor can be reprogrammed over the air through the (Microsoft patented through Nokia lol) radio processor, I think that it's very unwise to install GApps or any other apps that require any kind of system access or private data access. On wi-fi only tablets, which have no radio, this risk is much smaller, and the risk can be contained with some common sense. The sad truth is that you don't have any control whatsoever over a mobile phone, because the radio, over which you have no control whatsoever, overrides everything else. So the less interfunctional software you have on your phone, the better, and you have to realize that your phone - even when you've only loaded free and open source software on it - is never going to be completely safe and is never going to respect your human rights entirely.
Just configure your services so that Google doesn't get any privacy information. When they do violate your privacy - which they do - after you've denied them access through their own settings, at least you'll have a point in court if at some point the shit hits the fan (and sooner or later, it will).
The key thing is to check what's available for your device. Some devices, mainly from Samsung, Sony, Motorola and some Chinese manufacturers, are more receptive to custom firmwares than others. Although Google markets the Nexus devices as ideal for flashing, this is not always the case in reality, and it often takes a very long time before all the features of the hardware are unlocked in custom firmwares.
This is why the OnePlus devices are probably going to be a big deal, because they'll have Cyanogenmod 11 preinstalled, GApps optional. Although I really love the GUI feel and easy CLI system access (pure linux) of SailfishOS, I might get a OnePlus One because it's a newer device than my Jolla that has SailfishOS, which is my main phone. There certainly are limitations to SailfishOS for the moment, and I was definitely expecting a faster software evolution by the Jolla team.