Can I read my Gmail while traveling in China?

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.

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.

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Old (outdated) answer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.

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.

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.