Yes, you don't have to use Google. You don't have to use Windows either.
Nowadays, you hardly have to use windows, indeed. In big part, thanks to all the on-line companies which managed to turn most of the important stuff into on-line services accessible from any standard compliant platform, thus rendering the whole question of OS irrelevant.
But in a not-so-long-ago past, Windows was the only way to go because most of the software one needed only existed as win32 application, lots of the hardware one could buy only came with windows drivers instead of being a generic USB class with generic drivers, it wasn't easy to buy computers without windows and replacing the OS wasn't easy either, and Microsoft had managed to leverage their OS monopoly to almost get a monopoly in office suite (everybody considering Ms-Office as a de facto standard, which was problematic because not only their format wasn't standard, it wasn't even consistent or compatible between versions) (or, buy pushing their bundeled-in Internet Explorer, Microsoft could almost have managed to create their own ecosystem of weird microsoft dialects instead of the standard driven web that we know today)
Of course, today, thanks to on-line service and opensources equivalent like LibreOffice or Firefox (or Google's own Chrome and Google Docs), thanks to gizmo vendor using stuff like UVC (Universal Video Class) for their webcams instead of obscure proprietary interfaces, thanks to reverse engineering efforts, thanks to developpers paying for alternative OSes (including Google's own support of Linux), etc. You can go without Microsoft.
It took massive effort from every one *else*, and it took some revolutionary shifts in paradigms (on-line services making the OS irrelevant), before we reached a situation where you don't need to go to Microsoft.
Now compare with Google: You don't have to use google's stuff, and google is indeed making it easier for you, by making it as easy as possible to interoperate with their service. Their e-mail servers speak standard IMAP and POP, so should you decide to move to another provider, it's damn trival to get your mail with you. And the contacts are easy to export, too. Their chat system is using XMPP/Jabber, so it's possible to interoperate with any other fully complient XMPP chat provider that does support federated chat (basically anyons but Facebook. FB's XMPP is just a compatibility layer above their proprietary chat system and a doesn't not interoperate with anyone else). Their Google Docs documents can be exported both to industry standard (Open Document Foundation) and de facto standard (interroperate with MS-Office). Most of their software is availble as opensource. (Android, Chrome, lots of libraries, ...)
At no point in time have they done anything to prevent people running to other solution. They insist in trying to be as much interoperable as possible, and people stick to them because they are damn convenient.
About your privacy considerations : well if you really want to keep your life secret, nothing prevents you from using encryption. You can even send and receive encrypted mails through your gmail account as long as you're accessing it with some standalone IMAP/STMP compatible client (say Thunderbird). You can chat with encryption as long as both ends support end-to-end encryption like OTR (Off The Record - supported by the whole libpurple family like pidgin, adium, etc.). In fact it's possible to use Google services without revealing much of your private life. (Unlike facebook where it's fundamentally much more difficule to avoid revealing anything, due to the nature of their service).
Google has a core business - advertising. But pretty much everything else they do, they do it nicely - use standards, publish source, etc.
Of course they play nice, not because they're pure-hearted angels, but also to avoid alienating their user base and thus loosing ad viewers. But no matter what their motives are, they mostly stick true to their "do no evil motto".
The only point on which they do have an advantage to leverage: the size of their database. They have unbelievable amount of data collected from the web, from the streets, from stored content, etc. that they can use in creative ways. (For example, as mentioned elsewhere on this slashdot entry: statistical translation has been attempted before, but google are the first to have a nice implementation of it... because they can leverage all their huge data collection to provide the statistics powering the translation engine). For a newcomer, it's going to be difficult to gather the same impressive amount of data.
Their business model is not obvious to a normal person.
You mean, beside their constant advertisement for AdWords ?! I think if you missed that they are an advertising company, you need to be blind.