Let me start off by saying sometimes its good to have a weak password. When signing up to some weird website, I wont give a password that I use for important accounts.
Now say you have a password that you use for everything. All your email accounts, your online bank account, your mobile phone account and so on. You have the same PW because it makes things easy, like many people think. Then you sign up to some goofy site that has no real importance. For the user name you enter your existing email address, then give your usual password as well. Well now that goofy website can then try to sign into your email address, with the password you just gave them, and bingo they are in.
What do they look for when they get into your emails? Anything they can use. They look at your details to find out if you have another email address, and they get into that as well (even easier probably). Also they can request the for password or user name to be reset for other accounts. Now they can get into your paypal account or even your bank account all thanks to your email.
All this may be unlikely, but its so easy for them to do.
How to Secure Your E-mail Address.
How do you prevent this? Just use a password that is easy and different from your others. For example a sentence of something easy to remember. the longer your password the better. Try out this site HERE to find out how easy it would be to crack a small password. (please don't enter your passwords in this box, just use the same amount of letters/numbers or more)
If you have an email address and are very unlikely to forget the password, then make sure the security questions are completely random. You may have a good password, but if your security questions have the answers posted all over Facebook or public records, then someone can gain access to your account and lock you out of it.
How to keep your email safe from other people? Use crazy random long answers.
When the question is "where is your mothers birthplace" then answer "kfjoasdkfj[34u905u7314oij" or some insane thing you know no one can ever guess. It's easy to say "this will never happen to me" or "I don't have anything worth getting access to" but does that mean you still want someone else to have your email address, after all you will never know they have it.
It's your account and you should protect it.