"Google is unavoidable"
I thought so too. Till about November 2014. That's when I rejoined diaspora and found some awesome alternative services. Here's how I stopped being a Google fan boy and started living a life without Google

On the Web

On Desktop

On Android

On android phones it is a whole lot easier (than what I thought) to get rid of Google

Read more about f-droid and other recommended free apps

On Phone

Sometimes it makes sense to take out android entirely and replace it with actually "free and open" OSes like Firefox OS

Setting up F-droid and freeing android

Prism Break has a collection of applications like the above list. The list is definitely more comprehensive and accurate than this one.

Checkout projects like unhosted.org. Going indie is one of my 2015 resolutions (just created). I'm already independent of Google and Facebook and you can be too, zero cost.

Pablo also told me about NOGAPPS project which is "a set of applications and frameworks with the goal to fill the gap of missing gapps package"