Today, I removed Google Analytics from this site. I've been debating this for a while now, ever since the discussion of ad tracking that came with the release of iOS 9. I think it's unfair that I use Google Analytics to track visitors to this site but that I also block GA on my machine.
During that whole discussion, I went looking for alternatives, and I've been using GoAccess for a few months now in parallel with Google Analytics. Overall I'd say the results are vaguely comparable. GoAccess gives me higher overall numbers for pageviews and visitor counts, but that's a consequence of it running on the server and seeing the effects of browser pre-fetching.
Every night a custom script runs the numbers and spits out a directory with a few different reports for that day, and that week so far. It's a good system, and although it doesn't have the cool real-time features of Google Analytics, I found that that actually keeps me from constantly checking the traffic when I'm supposed to be doing something else. Although, GoAccess does have a live traffic CLI interface if I really need it.