> Every month, I pay my landlord (a professor; I'm his only tenant) with a check. I wonder what system would replace that, that would be significantly different from checks, but that my landlord could accept?
A standing order.
> Also, what if I run over someone's bicycle, and I want to give him a blank check to pay for it? Or, more realistically, what if I need to pay an individual that I have only just met more money than I have in cash?
If you're going to give black cheques away to strangers, why not just give them your bank card and PIN?
As for the second situation, I'm sure your dealer can wait a day or two. ;)