You are right in the fact that the amount of personal information they collect is appalling. Most importantly, they have the intent "to make sense of it all". Google has stated publicly its their intent to try and monitor people's behavior and habits, with the goal of optimizing the ads they serve you. This is only what they care to admit they use it for, in reality can be a lot more sinister. Google has FBI style databases on many people, that they have constructed through all the personal information they have accumulated from your gmail, youtube accounts; what and how you search for, etc.
Now as to the reason why a lot of this is free:
Its not just because they want to integrate everything to better study you. Its because their core business (adsense) brings in enough money for them to run all these pet projects. Their real intent is to basically slit microsoft's throat. They can afford to offer free office alternatives, free OS for computers, phones and soon to be server OS (what MSFT makes ALL their money from) because they have a different core business. Its the same reason why MSFT can plow billions into bing and keep losing billions on it, because search engine advertising is not their core business, and the reason they want into search is for the same reason google wants into software. Only, I feel google really has the upper hand, since google can offer a free OS, but there isn't exactly an analogy you can make with search engines. MSFT's attempt at this analogy is their whole "smart search" but most people at this point as google groupies, or groupies of other search engines (and its because of that brand loyalty that yahoo is still #1 in some Asian countries where google is in bing's position here in the US, why yandex is #1 in Russia, why france/brazil etc have their own market leaders, etc).
Google now uses some basic knowledge of you by fine-tuning their suggestions. If you search for something it will now automatically attach the city it thinks you're in, for example, if you are searching "chinese food" it will offer "chinese food greenwich" as a suggestion if it thinks you live in greenwich.
