I vastly prefer credit/debit cards - I have a record of exactly what was spent where & when. Cash just kinda tends to vanish into the ether without a trace. Not to mention, if I lose plastic, I'm not liable for fraudulent charges. If I lose cash, I am SOL.
Also, getting cash usually costs more - most of my banking is done with a credit union out of state. While there are some networked ATMs I can use without fees, there's not that many. So if I want to go plastic-free, it's going to cost me. And then we also go back to the possibility of stolen wallets and ether. I do have an account with a national bank, so plenty of ATMs there, but if I want to go shopping at Costco (where I can't use my debit card as a credit card), I get charged $0.25 for using my card as a debit card, so that's not exactly my primary account.
I use Paypal for lots of online transactions - and yes, I gave them my bank info. Never been a problem. Actually, it was really handy when my debit card vanished and I had to pay some bills while waiting for the new card - Netflix takes Paypal! Very handy.
And, if I'm doing a one-off purchase (i.e., not recurring, like Netflix), Discover (as someone in the other thread pointed out) has a deal where they can generate a one-time-use CC #. So even if someone steals that number, it won't do them any good. I know other banks have done that in the past, I don't know who all does now. Paypal used to, I don't know if they still do or not.
And stargazer pointed out about rewards - another reason I like plastic. My credit union even gives rewards when I use my debit card as a CC (so sign for it, not PIN). I like getting rewarded for buying stuff I was going to buy anyway.