I've been a moderately happy Chase customer for about 10 years now. I originally chose them because my father used it, and I was able to open a joint savings account under his checking account to avoid fees back when I was in high school. It was convenient from my parents' house, and it was certainly convenient in NYC. The addition of the Duane Reade ATMs was certainly nice.
I say "moderately happy" because, in general, my experience has been pretty ambivalent. I've had a few problems with Customer Service, but nothing major. There was a time where the telemarketers wouldn't stop calling even though I asked to be put on their internal "Do Not Call" list. (The Do Not Call registry wouldn't apply because we have a pre-existing relationship). The calls only stopped after I threatened to take my business elsewhere and make sure that they knew it was this particular CSR who didn't ensure I was on that list. I never got another call. I have two credit cards from Chase which I never use. In fact, most of the calls I mentioned above were about issuing me new credit cards, even though I didn't use the ones I had. ("But sir, this one is a Visa Platinum, the other one is a Mastercard, and even though you already have a Mastercard, this one is different rewards. And besides, it's free, so just take it".)
Chase's savings account offer a measly 1.24% rate right now, so I tend to use ING Direct with it's 4.35%. There are other options out there with even higher rates, but I've been with ING for several years now. As such, I generally don't keep much in my Chase savings account. It's sort of my "intermediary" savings account. I generally keep less than $1,000 in there, except when I have a large payment to make. For example, I have to make a tuition payment later this month, and since it takes 5 days to get money in and out of ING, I keep this money in my Chase savings. After all, 1.24% is better than nothing.
I did this recently, but unfortunately made the mistake of emptying the account entirely. Chase decided that this signaled my intention to close the account. (Curiously, they never closed my credit cards even though I haven't had made a purchase with them in years.) I only noticed this when my automatic savings plan failed because the account was closed. I called Customer Service and was told that I could only reopen the account in a branch. After I waited in line for 20 minutes, I had to make a deposit into the account in order to reopen it. (They couldn't just transfer money, because the account was closed). I literally deposited a dime - if I had a penny, I would have deposited that instead. I was told that the account would take 2-3 business days to be reopened. Indeed, every time I tried to add the account back on Chase.com, I was told it was closed. Finally, I was able to add it a week later - only to be told that it will show up on my online banking a week later.
In all of this, I've decided to close all of my Chase accounts and move to Citibank instead. Citibank offers all of the same features, and while they don't have all of the Duane Reade ATMs, they have plenty in the city and perhaps more outside of the New York area. Better yet, they offer an e-Savings account that earns 5.00% (even higher than ING Direct) with instant transfer between my checking and savings.
Chase made the last month enough of a hassle that I finally realized it can't be any more of a hassle to leave them. The moral is, if you aren't competitive on price (in this case, interest rates), you better at least make up for in quality of service. I recognize some of this "premium" is the convenience - but ultimately we also want a hassle-free relationship. You should make it easy, not difficult, to do business with you - otherwise even your long-term customers are going to leave.
I should also note that my experiences with Chase are not isolated. My father has recently had a number of issues with online bill payment and their customer service. Another friend told me about a number of issues he had trying to fund and then close accounts. When I told someone at work about my experiences, it was followed by a number of folks who had terrible experiences with their customer service.
This is a sad fact that the mobile carriers are finally coming to terms with in the age of number portability. It's significantly cheaper to keep existing customers than attract new ones. And yet, the worst thing that can possibly happen is that you alienate your existing, once-loyal customers. The cost of reacquiring a customer who feels wronged or hassled is infinite. You've all but lost us for life.
And yet, ironically, I'm willing to bet I have trouble closing the rest of my accounts even after I empty them.