Pretty much everything with a card with some exceptions
Rent is paid by check
some bills are paid over the internet (same principal, but different medium)
certain events like going to the bar or a show (or where I may consume lots of alcohol), cash only for security reasons (if I even do bring a wallet, its usually in my girl's purse or in a secure pocket in my clothes)
my favorite Japanese restaurant, they only take cash and they are worth it.