I've had a lot of calls from customers asking for help after reading about the Heart Bleed / Heartbleed issue.
Well there is really very little chance of YOUR password in a specific site having been compromised. BUT the recommendation from just about everywhere is to change your passwords.
There is no point changing your password before the site you are using secures their code, your new password would still be vulnerable. However there are plenty of sites that have information on the updates Mashable.com and many sites will email you when they have made the security changes.
Here is a link that explains how the bug works Howtogeek.com
Obviously you will have to make a note of all your new password and you may need to log into services, Apps and programs that use these passwords. For example if you use Outlook to read your email and you change the email password - you will also need to change it in Outlook.
If you have not already done so I would strongly advice you to use LASTPASS (or a similar system) to keep track of all your passwords. Lastpass now even has a security feature that will help you manage the password changes and what sites to change and WHEN. Don't forget to accept the password changes when it warns you. Lastpass even has a history button to show you the old passwords.
See Lifehacker.com for a tutorial.
And get your LastPass account here Lastpass.com/create_account