How do you manage passwords across SFDC orgs?

Use a password management tool like 1Password, Lastpass, or KeePass. I believe all of them have desktop apps, browser plugins and mobile apps with database syncing in one form or another (such as DropBox).

I prefer 1Password as it's plugins make it very easy for me to use multiple logins for the same site. When I go to login.salesforce.com I hit a hotkey and it shows all my SalesForce accounts and if I begin typing it searches the account names, then I can arrow down and hit enter (or just hit enter if there's only one result) to log in.

It's the only sane way I've found to manage 50+ Salesforce accounts easily.

I noticed in the Winter 13 release notes (page 204 of the PDF) there is a mention of "Environment Hub (pilot)". Worth keeping an eye on.

Starting in Winter ‘13, you can use the Environment Hub to view details of all your Salesforce organizations from one, central location. This can make administration much easier, especially for companies that use a large number of organizations for development and testing.

From the Environment Hub, you can:

• Register all organizations currently used by your company
• Automatically detect relationships between organizations
• View details about each organization, such as its type (for example, Development, Patch, or Release) and tags
• Assign one or more tags to any organization
• Filter organizations by tag

Environment Hub online help

I use the Google Chrome plugin: Force.com Logins

Not very secure, but easy for poping between a lot of orgs very quickly!

Also easy to export and import large sets to an XML document for easy transport.