I never had any trouble accessing the Internet, except that I could not always get to every site I wanted to (see this earlier post).
Accessing my virtual private network (VPN) was another story. Essentially, VPN allowed me to access the Internet through a U.S. portal. Otherwise I was accessing the Internet through a Chinese portal. (And I used VPN to access my company e-mail.)
Shanghai - VPN worked reasonably well. I was only dropped occasionally.
Jinan - VPN was the best here. I was never dropped.
Harbin - VPN worked poorly. I was dropped frequently, and for about a day early in our visit VPN did not work at all.
Beijing - At first VPN worked well, only dropping me occasionally. But for the last 2-3 days, it did not work at all. I don't know if this was a network quality issue, or a deliberate blocking issue. There were reports in the media at home that the Chinese government had further tightened Internet controls in advance of the 17th National Congress of the Communist Party of China which commenced while we were in Beijing.