I have both credit cards and a checking account with Chase and I've never had a problem with them. From reading the reviews, I think a lot of people seem to be angry about overdraft fees, which by the way, are disclosed when you open a checking account. Funny thing is, all you have to do to prevent overdraft fees is check the little box marked "No" when they ask for overdraft. Tada! They'll decline your transaction if you try to overdraw, problem solved.
Both banking and credit card customer service are great, the only reason I would say it's 'good' instead of 'great' is that it can take a while to get ahold of someone.
Their online banking and mobile apps are easy to use, and put all your credit/ checking accounts on one page. Also, if you have a Chase checking and want to pay your Chase credit card bill, the transaction is one of the fastest I've seen.
Also, there are A LOT of Chase banks in most heavily populated areas, as well as Chase ATM's. I switched banks when I temporarily moved to rural NC, which was a mistake. Switched back and haven't regretted it.