In an effort to avoid fees as much as possible, I now have nine bank accounts here. Most of them I've dropped because others have come up with better offers, though.
1. Standard Chartered. Better US$ cash exchange rate than the others due to waiving the Cash/Wire exchange difference, and because I got a Breeze account while it was still no-minimum-balance I have free domestic transfers and free withdrawals anywhere in China. Plus it works with Alipay/Taobao. Downside is they're getting popular and some branches are almost as crowded as ICBC/CCB/etc.
2. Dah Sing Bank. Free withdrawals anywhere in the world (ATM operator fees notwithstanding). Quick service (there's yet to be a single time I've walked into the branch and had to wait- it's always walk in-get 'er done-walk out). And they didn't charge me to issue an ATM card. But there's only a single branch in Shanghai (at least it's in Xujiahui).
3. Nanyang Commercial Bank. I can use any BoC branch for basic RMB stuff (deposits/withdrawals for free), so that's a plus. Free ATM withdrawals in China (and I can deposit cash at BoC cash deposit machines- no intercity fee if you're outside Shanghai, which is better than BoC does for its own accounts). Downside is you have to walk into one of their own branches to open an account and those are few and far between.
Meanwhile, BoC makes me irate, to put it nicely (they make me produce ID if I do anything with my NCB account involving a teller, and there are a couple of things involving on-campus services that I *absolutely* have to use a BoC account for), ICBC makes me feel neutral at best (seriously, why can't I switch from an RMB-only credit card to an RMB+foreign currency card without reapplying? But on the plus side, it supports PayByTouch) and I keep a BankComm account only for the RFID ATM card that gets me 40% off on the vending machines.
On the US side I just use Schwab.