I used to cut things much closer, with $500 in my checking and everything else in savings. I wasn't earning much from my job though, so even then, I was only ever able to amass about $4K in total. Still, I loved to play games to see how much I could transfer to my savings and just how low I could let my checking account get. ($1.15 is my personal best.)
Now, I tend to keep much, much more. Until I moved some of it into investments, I had well over $10K combined in all of my checking/savings accounts (it basically sat there for all of November). I'm trying to talk myself into keeping something closer to $4-5K, but it's hard for me to feel comfortable with that, given how much I've had to help my mom/parents the last year or two.
I had barely started my much-higher-paying tutoring gig when mom's chronic illness decided to really wreak havoc. Eventually, she was out of work for over 10 months with NO income whatsoever -- I ended up making several mortgage payments for my parents and paying for food, doctors' copays, prescriptions, etc.
Luckily, they didn't run out of savings and need me to step in until the super-busy "Spring Testing Season", so I was able to cash flow most of the expenses. BUT if they'd needed my help in, say, June through August...well...let's not think about that. Even with the big cash flow, it depleted my savings to less than $2K for a while.
So I now tend to err on the side of huge, heaping helpings of caution, even though I'd be fine with $500 or so if I only had myself to worry about.