I don't think there's any law against having lots of bank accounts. But what are you really gaining? Every new account is a paperwork hassle. Every new account is another target for con men who might steal your information and write bad checks or make phony credit card purchases in your name.
Yes, it's not unreasonable to have a credit card or two that you keep for emergencies. I'd advise anyone with running up debts while having no idea how you will pay them off. But to say that you might keep some credit available so that if you have a legitimate emergency -- like, say, your car breaks down and you don't have the cash to fix it and you can't get to work without it -- you have some a fallback. But do you really need ten credit cards for that sort of thing? And how much credit are they giving you on each card? I don't know how the banks work this, but I'd think if they're rational, they'd consider your total credit before giving you more.
I have three credit cards that I use regularly -- two personal and one business. And I find that a real pain to keep track of, to make sure that I keep each one paid by the due date and to keep a handle on how much I owe and so forth. I can't imagine trying to deal with ten. I suppose you could just stuff all these cards in a drawer and only use them in case of emergency.