About two years ago I proclaimed my intention to eliminate as many of Google's services from my personal work flow as possible. About 10 months later I announced my failure. However, I didn't really fail as I never gave up. Today I am mostly Google-free in my personal work flow. My employer utilizes Google Apps extensively, so there isn't much I can do about that.
The first change I made two years ago was change my default search engine from Google to Duck Duck Go. That change stuck and I rarely need to do a secondary search on Google. In fact, DDG as always done a much better job of filtering out the spam blogs that tend to gum up the first page of results on Google.
Mail was a major sticking point for a while, mostly because I had a web host that had puny email offerings, but I didn't want to undergo the hassle of moving 5 or 6 web sites to a new host. So I kept trying various email services and never being happy. Once I finally gave in and moved my web sites to a host that provided reasonable email storage it's been fine. ODonnellWeb email is all run from the web host, so I don't need Gmail at all. I had a Gmail account from back when they were still very hard to get, so that address is in 1000 places. I forward Gmail to my domain account and change the addresses as I can. However, I suspect that Gmail account will always exist, but I just won't use it. I'm using my old 1990s Yahoo address as my sign up / throw away email account.
Calendar has been another PITA area. I've installed several open-source calendar tools on my web account, only to find them all lacking in some way. For now I'm on Yahoo Calendar, which isn't ideal. However, the Caldav syncing seems to work more consistently than Google's ever did so I Caldav it to Thunderbird on my desktop and the stock calendar on my phone so that I don't need to use the Yahoo Android app for anything.
Photo sharing is another area where I've been able to mostly get rid of Google. I do cheat and let photos from my phone backup to Google, but they stay marked as private. I have gotten lazy at times at shared photos from Google+, so I'm trying to not do that. I have an open source script on my server that indexes and displays photos. It's not as pretty as Google+, but it's functional enough for the relatively few photo albums that I share. I did check out the new Flickr, which is very nice. But then I'd still be depending on a service I don't pay for.
I have an Android phone and a Nexus 7 tablet, so it's debatable if I've removed Google from my life at all. At least they are open source though. I think the lesson here is that if you are willing to learn to work differently, not necessarily better or worse, just different, you can mostly avoid Google products online.