Recently I was in Spain and I withdrew all money from my account while returning. At night I checked my balance online and it showed -250 Euros. Is it possible? Should I have done something about it?
Of course its possible. Under what terms and with what fees depends on your bank/country regulations, but generally speaking - loaning is the major source of income for banks, especially short-term account overdrafts (which is essentially a loan, usually at a high rate).
In the US you can (now, since the new regulations kicked in) instruct the bank not to pay checks/decline debit card purchases if you don't have sufficient funds on the account. Otherwise you can instruct them to pay (at their discretion) to avoid bouncing checks, and accept NSF fees (usually pretty high). Some banks provide overdraft lines of credit (then you won't have NSF fees, and will just pay interest when tapping into that line), others provide option to automatically withdraw the missing amount from a linked account (checking or credit card).
If the answer were "no," you still found the 'black swan' type exception that proves the answer to be "yes," right?
My experience is this - again just my experience, my bank - When by balance goes below $10, I have the account trigger an email. I wrote a check I forgot to register and subtract, so the email was sent and the account balance in fact showed negative. I transferred to cover the check and the next day, there was a history that didn't go negative, the evening deposit was credited prior to check clearing.
I set up my bills on line. I set a transfer in advance for the same dollar amount as a bill that was due, e.g. $1000 transfer for a $1000 bill. I woke up to an email, and the account showed the bill was paid prior to the transfer. So one line showed going -$900, and the next line +$100 after transfer. Even though it's the same online process. Again, the next day the history re-ordered to look like I was never negative. But even on a day I know I'm having payments issued, I can never just ignore that email.
The first time this happened, I asked the bank, and they said if the negative went until the next day, I'd get an overdraft/short balance notice.
This is a situation to ask your bank how they handle this.