I've been using PasswordMaker (http://www.passwordmaker.org/) for years to generate most of my site-specific passwords when needed. PasswordMaker uses a master password together with a site's domain name to hash a site-specific password. It has Chrome and Firefox extensions for filling in the password fields with one button.

Unfortunately, by default it uses MD5 and 8-character passwords. I always set this to SHA256 and at least 12 characters when first installing the extension on some device/browser.

Most sites play well with this, but there are exceptions: having to change a password is a bit ugly when the passwords are generated from a given master password and the site's domain name. A more common problem is when a site refuses to accept certain characters in the hashed password or when a site requires some number of digits and uppercase letters, for instance. I currently just store these exceptions with Keepass.

I see 1Password being mentioned a lot but I started using PasswordMaker and Keepass well before I'd first heard of 1Password so I don't know how it might compare.