US here. Checks are, IMO becoming less common, but they are still sometimes necessary. More and more businesses are taking debit cards, so people have the option of paying with cash, credit card, debit card or check. The last time I used a check in a store, about a year ago, the cashier had to ask her supervisor for help, but I think she was relatively new to the job. However, the salon where I get my hair cut will only take cash or a check, same with the sub shop down the street. I know that credit card companies charge the stores a percentage of each sale--if the same is true for debit cards, it's understandable that a small business, running on a small profit margin, doesn't want any part of that profit going to the debit card company.
Larger companies tend to want to use direct deposit for paychecks, but there are fees associated with this, so smaller companies sometimes still don't even have the option, because it would cost them too much money. One small company I worked for, when pressed for direct deposit, said that they'd do it, but would charge each employee $1 per direct deposit, to offset the associated fee. Since it seemed silly to have to pay to get your paycheck, that idea died a quick death.
Also, there are various laws about paying employees--these vary from state to state. But many states have regulations that you cannot force an employee to have a bank account in order to be paid. This stems from the fact that some people with terrible credit ratings have a hard time finding banks that will allow them to open an account. Or that many banks require minimum deposits in order to avoid paying monthly fees--people at the lowest income levels can't afford the fees, nor can they afford to leave $1000 just sitting in a bank account to avoid fees. So companies are, in many places, required to offer a paper paycheck in addition to direct deposit.
You can make some payments electronically--my electric bill, my internet company, my phone company. But the oil company (we have oil heat) needs a check or credit card. My bank charges $5 a month if you want to make on-line payments through the bank. On the other hand, I can go to the websites of my utility companies and make a free on-line payment there. Making an electronic payment to another person--it might be possible, but I have no idea how one would go about doing that. If I need to give someone money, it's cash or a check. I have to pay my rent by check. I suppose I could use cash, but I wouldn't feel comfortable mailing that much cash.
My current landlord is a guy who owns a few houses for rent, but my last landlord was a huge property management company. When I asked about some sort of direct payment instead of having to write and mail a check every month, it took two days for them to figure out that I could allow them to set up an automatic withdrawal from my checking account every month. The problem with that is that there have been many problems with such automatic withdrawals--it can be very difficult to get the company making the withdrawal to stop and the banks claim they can't do anything about it. If I could have been in charge of making the direct payment, I'd have gone with it. But I really didn't like the idea of allowing that particular management company access to my money.
I think the banks here have a variety of electronic systems, which have varying degrees of compatibility. And my bank's on-line services have issues. I don't know what the problem is, but I have to reset my password constantly (like once a month) and every single time they "upgrade" their system, I have to call and go through setting up the on-line part of my account all over again. There's no way to do this without speaking to a real live person, and I appreciate that they are trying to keep things secure, but it's a hassle.
And there's a general fear amongst a lot of people that on-line banking isn't very secure and your account could be hacked and you could lose all your money.