Recently google was subject of hacker attack. Actually, one friend of mine had it gmail account hacked. He not only lost access to his emails, fraudulent emails were sent to his contacts asking for money. It said he is stuck somewhere in Europe and needs money. I got one of those emails, but I knew it was phishing email and his email was hacked.
It is very usual to have many emails e.g. yahoo, gmail, aol, etc etc these days. It seems convenient also to keep same password for all system as it makes it easy to keep track of. But it can be very dangerous as well. If a hacker gets to know one password, he can gain access to all your emails and you have no way to reset as your backup email will not work either.
So although convenient, it is mandatory to keep different password for different systems. Also it is recommended to change the password every so often.