Many things may be purchased or accessed only via debit cards, purchasable at the subway ticket counters, out of machines, and within the buildings of major employers. Public phones do not take money; they require a Telecarte (phone card). In some areas, taxis require cards. Most of the vending machines inside major employers require cards.
Employees at employers large enough to have cafeterias probably have meal cards. If you are a visitor at one of these cafeterias, some places require you to pay cash while others require that you buy a daily meal ticket for the cafeteria (or eat elsewhere). More than likely, visitors will be charged full price; the employee discount is usually seen as an employee benefit. It's kind of silly with contractors, since they are usually billing back to the company, but that's how it works.
Note that each vendor or type of purchase requires a separate card.
There is usually no way to directly get a refund on unused portions of cards when you leave. So don't go for bulk discounts or convenience unless you are sure you will use it, or have someone to sell the card to, or pass the card to (as a gift, fellow employee, whatever).