This article was written in 2016. Information below may be outdated or inaccurate.
Google and all associated services have now been completely blocked in China. You can find more up-to-date information elsewhere.
The relationship between Google and China has never been a smooth one: the former's aim is to make information universally accessible, while the latter wants to restrict it as much as possible
Whilst Google and its related services (Gmail, Calendar, Translate, Maps, etc.) are not officially blocked in China per se, they are purposefully crippled by the firewall. This is not only because of a long-standing argument about censorship between Google and the Chinese government, but also because the Chinese government prefers that its netizens use services that the government can control, filter, and profit from.
The full Google vs China story goes as follows:
A while ago, China wanted Google to censor google.cn's search results, but Google's anti-censorship stance meant that they wouldn't play along. At first they considered it in a few select cases: for example, Googling 'Tiananmen Square' in China did not result in the infamous tank man photo, but search the same term from everywhere else and you got nothing but that photo (since that is the event that Tiananmen Square is most famous for outside of China). Later, Google straight up refused to censor search results at the government's whim.
As a result, in order to avoid the Chinese government basically blocking Google entirely through the Great Firewall, in November 2010 Google shut down google.cn, citing its anti-censorship stance and the discovery of a targeted cyber attack on its network infrastructure. 2 months later they started forwarding all Google search results from China to google.com.hk: Google Hong Kong. Hong Kong is technically part of China, but is considered a Special Administrative Region, and the internet there isn't censored. So, basically users get the full, uncensored search results, but most of the time if they clicked on a result, they wouldn't be able to access the actual sites because they were still blocked on the mainland.
In retaliation, the Chinese government basically crippled Google in China by making it very slow and temperamental (via intentionally dropping packets when communicating with Google sites), but not blocking it entirely. The Chinese government blames Google for the poor performance, Google blames China. The Chinese government did this not only as a countermeasure to Google forwarding search results to Hong Kong, but also to encourage Chinese netizens to move away from Google services (which they've proved they can't control) and towards Chinese alternatives which are controlled and monitored by the government, and which make money for the government (Baidu, Weibo, etc.).
By doing it this way, the government can also claim as their official stance that they haven't blocked Google - as they have with Facebook, Twitter, YouTube and many others - since the site will still load most of the time - even if it's next to unusable for those that rely on it.
Now and again, during times of particular political sensitivity - such as directly following the Communist Party's 18th National Congress in China, during which the party's new leaders were appointed - Google is blocked in its entirety.
Accessing Google and their services through a VPN avoids the packet-dropping problem, and gives you the performance you'd expect on these sites.