My experience with China's internet has been to have alternative solutions ready if you need access to Google's services.
You can use Google's Transparency Report for China to determine the current status of Google Services in PRC.
Currently, it is difficult to access Gmail, and many other Google services, in mainland China.
If Gmail is a critical service to you - have a backup plan.
Here are some solutions that have worked for me and others.
Have your Gmail forwarded to another service such as Microsoft Outlook or Protonmail .
If Gmail is inaccessible, you can check the other service for email.
A VPN /Proxy
Server is also another solution that others recommend - but China has occasionally blocked VPN traffic as well.
However, again it is another option to consider.
Note that as of early 2017, China has started blocking VPN providers and is reportedly attempting to ban all VPN providers in the near future.
Keep friends / family informed.
Let them know there is a possibility that you may lose access to email.
Have access to other means of communication like SMS or other secure messaging applications like WhatsApp or Signal.
travel.stackexchange.com/users/918/vcsjones
Because this question appears as one of the first suggestions on Google, I thought I would give an updated answer as of July 2019.
You cannot access any Google services in China without a VPN or a proxy service.
The only site that works is www.google.cn which I do not think many foreigners would want to use considering even the domain itself is not registered under Google even though is connects to an old Google China website.
It is easy to get a VPN service though you need external payment methods like paypal to pay for this services.
Edit: The Chinese government is doing a crackdown on VPNs that would see them completely shutdown by early 2018.
Apple removed popular VPNs from its China App Store in line with the government crackdown.
travel.stackexchange.com/users/31484/Zack
The short answer is, "yes, in most places at most times."
But there are some important exceptions.
China occasionally gets into "tiffs" with Google, or other Internet providers, which could cause a service disruption.
Also, there may be a crackdown against the internet generally, possibly including email.
Here's an example: http://moconews.net/article/419-china-cripples-android-with-fitful-blocks-of-gmail-market-apps/
As to places, China is a large country, and some places are less developed than others, with fewer T-1 lines, towers, etc.
Also, in politically sensitive areas like Tibet and the Uighur northwest, there may from time to time be a crackdown directed against the local population (and their communications), that will affect "innocent" foreigners as well.
travel.stackexchange.com/users/788/Tom Au
We were there in December 2014, absolutely no Google services of any kind worked.
That included Recaptcha.
We've been there multiple times since, still absolutely nothing Google, including the update my Android phone was trying to download.
Edit October 2019:
Nothing has changed.
Anything Google requires a VPN and they're getting more and more troublesome.
Strangely, it has behaved better in the morning (China time) than the evening.
Old (outdated) answer
It's never failed me over there.
Beware, however, that a SSL certificate failure results in nothing but an error message.
On a Chinese computer (internet cafe) the error was entirely in Chinese.
Since I don't read Chinese the result was totally cryptic.
What actually happened was the computer's clock was exactly 3 years in the past.
The last couple of times I've been there Google itself
was unusable, though.
travel.stackexchange.com/users/1764/Loren Pechtel
I'm surprised no one suggested using Tor (and Tor Browser) to access blocked internet sites, services and applications from China or from anywhere else in the world.
The Tor Project https://www.torproject.org/ provides a solution against blocking by authorities.
Either you can configure your browsers and applications to route traffic through Tor or you can download and use the Tor Browser, which is based on Mozilla Firefox.
Update: as public Tor relays are likely blocked by China, you can use bridges to connect to the Tor network.
travel.stackexchange.com/users/72137/Mcload
You can also connect to the Internet via a satellite, e.g. using a satellite phone.
As mentioned here: For many years satellite phones have been able to connect to the Internet.
Bandwidth varies from about 2400 bit/s for Iridium network satellites and ACeS based phones to 15 kbit/s upstream and 60 kbit/s downstream for Thuraya handsets.
Globalstar also provides Internet access at 9600 bit/s—like Iridium and ACeS a dial-up connection is required and is billed per minute, however both Globalstar and Iridium are planning to launch new satellites offering always-on data services at higher rates.
With Thuraya phones the 9,600 bit/s dial-up connection is also possible, the 60 kbit/s service is always-on and the user is billed for data transferred (about $5 per megabyte).
The phones can be connected to a laptop or other computer using a USB or RS-232 interface.
Due to the low bandwidths involved it is extremely slow to browse the web with such a connection, but useful for sending email, Secure Shell data and using other low-bandwidth protocols.
Since satellite phones tend to have omnidirectional antennas no alignment is required as long as there is a line of sight between the phone and the satellite.
travel.stackexchange.com/users/14104/Count Iblis
I read in some places that Gmail.com is sometimes blocked. Is there a workaround so that I can access my email while I am in China?
Can I read my Gmail while traveling in China?
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<china><internet>
travel.stackexchange.com/questions/2550
travel.stackexchange.com/users/297/Dani van der Meer
It is difficult to access any Google services in China without a VPN or through the Tor Project, which is based on Mozilla Firefox, but you can use Google's Transparency Report  for China to determine the current status of Google Services in PRC. There may be additional temporary crackdowns in sensitive areas like Tibet, which could also affect foreign travellers. Have a backup plan like SMS or a secure messaging application, or use a satellite phone. Equipping yourself with a backup for communication or connecting to the internet is considered advisable when travelling to China. Google and internet services are often blocked, as are VPNs. Whatsapp, satellite phone and the Tor Project are spossible alternatives. The situation may be even more difficult in politically sensitive areas.
Using Google services in China seems to be difficult, at least at some of the time. When travelling to China it is advisable to have a backup plan, like Whatsapp or get a VPN. However, VPNs may also not work. Check Google's Transparency Report for China to find out the situation before travelling. Alternatives to a VPN include the Tor Project and a satellite phone. It may be even more difficult to connect to Google in politically sensitive areas.