Recently a friend owed me some money and she wanted to send it electronically, but using the standard way (interac e-transfer) costs $1.50 and paying that much for a simple transfer really bothered me.
I tried thinking of a better way and realised that I can pay bills directly from my account for free, and so could she! So I gave her the account number for my electricity bills and she was able to pay directly into that, which is the same as paying me back.
For it to work you have to at least trust the person enough to give them this rather benign piece of information.
If you want to give out your credit card number then you can also do cash transfers if one person pays into the card, giving it a negative balance, and then you make a cash advance. With my card, anyways, I don't get charged any interest if I have a negative balance. Since there is no limit to how much money you put into a card I imagine that you can transfer large amounts this way as well.
Once you set up the payment in your account online you can also do automated payments and there is no password that you have to worry about.