I'm traveling to china for a couple of weeks for work. I don't do anything where information security or intellectual property is a huge concern, but I do want to be in touch with the home office so to speak and also with my family. Do major popular western web services e.g. Gmail, Skype, Dropbox work in China or does the 'great firewall' make then mostly useless?
Fret not, travel.stackexchange.com works just fine :D
For other services, however, currently there are over 2700 sites blocked in Mainland China.
Wikipedia maintains a list of popular sites or services blocked in mainland China. Pretty much all Google services, Yahoo, Dropbox, Facebook, Twitter, Youtube and more - see the list for details.
I can confirm when I was in Beijing recently, I tried a lot of major ones on that list, and pretty much anything useful was blocked (although Bing was only partially blocked).
I resigned myself to just watching TV, and then realised my Skype was online! I tried it, and sure enough the service is active - and I was able to call New Zealand, however there are other restrictions on the service in China. I'd suggest having it preinstalled.
The Wikipedia article on this subject is often incorrect. For up to date info on which sites are blocked, I suggest you look at https://en.greatfire.org/ who actually test the sites availability.
The main ones your will miss are Google (everything including Gmail and Play App store on your phone), YouTube, Facebook, Twitter, Blogger, Blogspot, Wordpress, Vimo, Slideshare, WSJ, NYTimes, and most popular porn and gambling sites.
Yahoo! and Bing do work in China but are subject to censorship on some search terms. Dropbox does work if you have it installed. I use it all the time.
Good ideas if coming to China: register a Yahoo! mail account and temporarily redirect your Gmail to Yahoo!. Get used to using bing.com to search instead of Google. Entertain yourself on Youku.com instead of YouTube - China has funny cat videos too (search for 有趣的猫).
If you really need to get on a blocked site, it is relatively easy to install a VPN on your computer and phone. They cost just a few dollars a month.