Depends which cryptocurrency you’re talking about. Businesses would not want to take most cryptocurrencies. Why would any business want tokens from Factom or Pylon Network (unless they participate in the blockchain solutions these tokens provide)?

Assuming you mean cryptocurrency designed as substitutes for cash, e.g. bitcoin, I’d say the biggest driver for a business to accept cryptocurrency is cost and speed compared to conventional electronic payments.

When you accept credit cards, you need to pay fees, e.g., $.09 per transaction + 2% fee for a low-tier merchant. Compared to $.01 cost of a single payment using LTC or $.00004 cost of a single payment using XLM. Those are just examples to show how much less expensive those specific cryptocurrencies are — depending on the specific charge, the costs will differ but overall, at least with LTC and XLM, you almost always save a lot versus the same transaction using bank or credit card.

Also, with cryptocurrency, you can transact phone-to-phone via QR code. No expensive point-of-sale equipment needed, though you may want to invest in an API to communicate between the blockchain and your business’s systems if you need to automate your record-keeping and/or business processes.

Further, with cryptocurrency, the transaction goes through instantly, instead of 1–3 business days when using credit or debit card. Little-known fact: debit and credit cards don’t pay the merchant immediately. The bank or credit card company vouches that the funds are there, which gives the business peace-of-mind knowing that as long as the bank or credit company is trustworthy, they’ll have the money within a day or three. This lets business accept your credit or debit card just like if you’d paid cash, because the credit card company or bank has already assured them the money’s going to be there.

I’ll give you a real-world example. I went on vacation recently and went out with a friend to get ice cream for everybody on the trip. When we got to the ice cream store, we discovered it accepted cash only. We had no cash. We never carry cash, as a habit. We went to the ATM a half-mile away and the machine was out of order. Next closest ATM was 2.3 miles away, so we went back to our vacation house to get cash from the others. If that merchant had a bitcoin wallet, we could’ve paid for our ice cream immediately and gone on our merry way. If not for the 10 people depending on us to get them ice cream, we would’ve just said screw it and spared ourselves the calories, and the merchant would’ve lost our sale.

That said, IMO the value of cryptocurrency for business is not as a payment system. It’s in leveraging the benefits of blockchain to streamline operations and cut costs. Whole different question and one many other Quora writers have addressed in great detail.

To me, the original question is like going back to 1992 and asking “why would a business want to accept email?” Or going back to 1980 and asking “why would a business want to accept a desktop computer?”

Email was quicker, less expensive, and less complicated than paper letters, telegrams, and faxes. Desktop computers were smaller, cheaper, more adaptable, and easier to fix than mainframes and people. That didn’t mean paper letters, telegrams, faxes, mainframes, and people weren’t important, and that didn’t mean early email and desktop computers were great. But email and desktop computers had certain advantages over the other options, and over time, as the tech got better and more businesses saw value, they became commonplace.