No cash is necessary for most people. In the modern day in the US there is no need to keep paper currency around for emergencies; any sort of emergency that knocked out all of the ability to use plastic (ATMs, credit cards, etc.) for an extended period of time AND knocked your bank out of service would be of the level that cash might not have any value either. Your $100 of cash for natural disasters is likely more than enough, and even that I wouldn't necessarily consider a vital thing in this day where even a major natural disaster probably isn't going to have too much impact on the financial sector outside of the immediate area (that you should be exiting quickly). Keep however much cash around that you need for day to day cash expenses, and that should be enough.
The level of emergency that would suggest cash being needed would probably need more than you'd actually want to keep around, anyway - i.e., a complete collapse of the American or World financial system would imply you need months' worth of cash. That's just not feasible, nor is it practical financially. You should have your emergency fund making at least a bit of interest - 1% or so isn't hard to get right now, and in the near future that may increase substantially if interest rates go up.
It also would make you a substantial theft target if it were known you had months' worth of cash around the house (i.e., thousands of dollars). Safes don't necessarily give you sufficient protection unless you've got a very good safe - commercial ones are only as safe as the ability to crack them and/or transport them is.
Now, if you find yourself regularly out at 2am and run out of cash, and you live somewhere that ATMs don't exist, and you find yourself needing to pay cab drivers from time to time after a drunk bender... then I'd keep at least one cab's worth of cash at home.