This page is about holding money, and paying with money.
When the money is kept, it needs storage. Where? How? etc.
When something is bought, a payment must take place. When something is bought from far away, a far-away-payment must take place. How? With what cost?
These are the issues relevant to money itself, mostly irrelevant to how it is earned and for what purpose it will be used.
Another page, at this site, discusses Finance. It is relevant, but different. Together, these two pages cover, if not replace, the functionality of "banking."
There is a social aspect of money. Islam requires that, every year, a small fraction of a person's wealth is distributed away, to the needy - starting with your relatives, and neighboorhood. This has its strengths, as a social-welfare policy. You may read further about No Taxes! Yes, Zekat!, including pointers to other, optional acts of mercy, that have developed from Islamic roots, and have been exercised/realized through ages, in the Islamic world.
The zekat is the only required - as enforceable by the society. The others are the individual's preference, about optimizing his/her, the-other-worldly gains. The existence of zekat means that, when you store money, without any business transactions, your money decreases, every year, little by little. This may motivate doing business with your money, rather than keeping it idle, for many years.
I have designed several ways for pocket-to-pocket money transfer - and with safety built-in, to very precise extents.
No need for credit cards, in some cases, even for banks - although some of the systems I designed benefit from such backing institutions.
One simplest example is: Carry cash. Let the serial numbers be known globally ...
In this section, I present one of the simplest money-ownership systems I have designed: mZip.0.
Storage: Hold cash in your pockets. Let the serial numbers be known globally - including by the state that issued it. This not only, is against theft and counterfeiters, but also against so many other crimes.
Payments: When buying something, pass the cash, physically, to the other side, and electronically record this transaction (i.e: the change of ownership of that money), inform the state that issued that/those cash/banknotes, about the money transfer. This is very easily automatizable.
e.g: A gadget that is pluggable into a cell phone, or to some palmtop computer, etc. The gadget is for scanning each money-note that is transferred. In fact, an electronically-active wallet, could feature further security functions (as a safe), and it is probably easier.
Remote payments, require further thinking - as it is, because Islamically there is the consideration of sufteje. Three of the four widespread (if not the only four alive) interpretations/sects (except the hanbelis), consider sufteje as to-be-avoided.
The base for avoiding is expressed as gaining an advantage in return for lending money.
But if the swap happens at the same moment, I then reflect, then there should be no problem.
This suggests the Islamic hawale.
For example, if 100 people at a variety of locations want to pass money back and forth, and the software arranges a full-loop so that each cent is transferred to the desired destination at the moment the transaction is executed, then there is no question of anyone lending anything to anyone, at all. Right? (Criticisms always welcome. In fatwa-like issues like this, I would especially not want to overlook any detail/point. Any (other) points to consider? Please be specific. Give the Islamic/fikih topic you are referring to.)
For remote-payments, some buffers could be useful, and that is easy: In a world where a lot of corporations are multi-national, and/or have mutual agreements, having transactions worldwide. If branches of a corporation do not care at what location the corporate's money resides, the corporation is essentially ready for smoothing out momentary transactions - without any cost to anyone involved, and nobody lending anyone any money.
In the limit, if some localities are to be paid a lot, the system may be blocked - just like being caught in crowded traffic, although the other direction has almost no traffic. (In this case, actually it is because the other direction does not have traffic, that the blocked one is blocked.) One way of breaking this could be if the payment-recipients may willingly let keeping their money in some other place(s) around the world (still, their own accounts, transferrable at any time to any non-congested direction), at least for some time. Not a major problem, I think. Hardly anybody eats up all the money he/she earns that day.
I discuss a few other ideas about remote-payments, in an internet wish-list. That page is not exclusively about this topic, but the relevance is valuable.