If I'm logged onto facebook, can someone log onto my account from another computer in the house?

[bluebird]

Yes
but Facebook introduce 'login approval'
only the certain useruse Facebook

How to: Activate Login Approvals on Facebook
Facebook introduced “Login Approvals” back in May 2011. Login approvals is a Two Factor Authentication system that requires users to enter a code that Facebook sends to their mobile phone via text message or via a code generatorfrom inside the Facebook mobile application. Users will be asked to enter a code sent to their phone via text message anytime they log on to Facebook from an unrecognized computer. Once the user enters a code they will have the option to save the device to their Facebook account so theydon’t have to enter the code again in thefuture.
One of the biggest questions we receive from our clients is “what happens if oneof your community manager’s personal accounts get hacked?” This is an extremely important and understandable question. After all, our community managers have the keys to their brand; if they get hacked it leaves aclient’s brand vulnerable to some big trouble. After looking into a variety of different solutions, we decided that is was best to initiate a mandatory Two Factor Authentication on all employee accounts that have access to any client brand pages.
Having a Two Factor Authentication gives our clients a sense of safety and confidence in the security precautions our agency is taking to protect their brand. You don’t have to be a community manager to activate Two Factor Authentication. The feature can be used to protect your personal data, photos, and credit card information on Facebook. Here’s how you can set up theTwo Factor Authentication in under five minutes:
1. Go to your account settings page.
2. Click the Security tab and hit “edit” under login approvals. Check the box to activate.
3. Enter in your cell phone number after you read about the Login Approvals feature.
4. Check your phone for an approval code, enter it on Facebook.
That’s it, you’re all set. The next time you log on from a different computer or mobile device you will be asked to enter in a code sent to your phone. Thankfully this is only a one time thing so it won’t get annoying once you create a profile for the specific device. In four easy stepsyou can improve the security of your personal data drastically

[Kevin Bramble]

depends on your internet settings, history etc if u have your history enable or sometimes facebook prompt u "do u want internet explorer to remember your password"? if u choose yes then whenvever again u go to log in faceboom once u click your arrow in the box to type your password it would automatically pop up in the box cuz internet explorer asked u if u want it to remember your password but if u don't want that then jus go to internet option/setting on your browser and delete history this will delete all internet data including your password that internet explorer remember.