Google Chrome (based on 'Chromium') is a good browser. If Google privacy is a worry, then there are other browsers around that use the same design/engine as Google Chrome. Comodo Dragon for instance.
Browsers based on Chromium have a sandboxed structure. This helps to make them more secure as regards infections that might be encountered while browsing the Internet. Flash Player, a possible source of infections, is included within Chrome's sandboxed structure, so an added security feature. No need to worry about Flash Player updates if using Google Chrome. It is automatically and quickly updated by Google. So, as well as Google Chrome being a fast browser, it does also include some hidden advantages that Firefox doesn't have at present.
As regards privacy, I think the trouble is that, whether Google products/services are used or not, our tracks are all over the Internet anyway. Any site visited includes trackers that interlink with each other no matter what browser is used. This can be reduced by using anti-tracking extensions or other measures but I know from experiments with 'Lightbeam' (an extension available for Chrome and Firefox that shows who is tracking you) that it is just about impossible to block Google and other trackers altogether.
So, Google Chrome or not, Google and other companies will be aware of where our IP addresses have been. They are only interested in the IP address though, not us as people with names and addresses. I think it has to be accepted that if we use the Internet we (our IP addresses) are going to be all over the place. Not sure there's much to be gained by avoiding Google products and services.
I mostly use Firefox but Chrome is installed as well and sometimes used. I use an external sandbox though, so Firefox too can be run sandboxed for added safety.
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