Is it possible for someone to hack say your Facebook Acct or games that you play and access your other private accounts even if the passwords are different??
Answer on What are ones chances of getting hacked? or having someone steal your identity?
That depends on a variety of factors.
For example, you don't mention how they hacked your account. If your account gets hacked because you used a weak password and they just happened to guess it, it likely won't affect your other accounts (assuming your other accounts have stronger passwords).
However, if you get hacked because a virus got onto your computer and logged all your keystrokes, then every account you've used since the keylogging began is at risk.
And then you have the situation where many people tend to have a "root account". For most of us, this is our primary email address. If you forget your facebook password, facebook will likely send the new password to your email address. If you forget your account for an online game, etc, many things are just reset through the email address you gave when you signed up. Thus, if this primary email account gets hacked, it's relatively easy for a determined individual to go through the history of past emails, see which accounts you have that are linked to the email, and then use the "forgot my password" feature to gain access to those accounts.
As far as your chances of being a victim, it depends on how security-conscious you are. If you keep your computer up-to-date (by installing all the updates for Windows, your web browser, Flash, Adobe Reader, MS office, etc), you're familiar with basic security principles (don't run unknown executables, use a strong password, don't use untrusted wireless connections, etc), and you're familiar with social engineering scams (phishing emails, etc), then your chances of being hacked are very small.
On the flip side, someone who doesn't follow the basic security principles is liable to get hacked relatively easily. For instance, World of Warcraft accounts tend to get hacked by the minute, because too many users are ignorant of how to remain safe on the internet.