You can be successful with your product on the WWW without employing any Google services, being totally independent. If people and other sites like you and link back to you your traffic will quickly skyrocket—which feels natural. You are not obliged to use any Google service like GA. Just use the Internet and its open standards and you are ready to go because Google left the Internet's core like it is and didn't build a walled garden around it. That's the great thing about the web: it's decentralized and everybody can contribute, Google haven't tried to change this. That's why I don't like the native app trend with the appstore, all the innovation the Internet brought us are vanished by one central and strict entity and nobody cares, Android at least tries to emulate some parts of the net (i.e. by using intents, allowing multiple appstores, with the open nature of Android, etc.), Google is regarding their marketplace Play much more relaxed than Apple.
Looking at the Appstore or the Facebook API, there are so many rules which don't follow any of the core principles of the Internet. You have to play by these rules otherwise you are banned or completely and utterly dependent of one single entities. Moreover, if you then play by Apple's or Facebook's rules you still do not get the impact as from Google traffic-wise.
Ultimately, Google haven't entered the Chinese Market which shows the company's values. Every larger western corporation have build joint venture based branches in China—every corporation, except Google—and that's distinguishes Google.
