I need a single-sign-on solution for a bunch of web-based apps

are all the apps within the same location? Did you create them?
You could use Third "party" authentication. meansing access to each app if a "token" is not present presents a form, or redirects to one that validates and passes the token back.....

What is your current method, each has their own user list?

In a case where a single signon you have to work things out whether the same user will have the same rights across all apps, or whether the user will have granular access meaning each app the user might have different rights.

whose apps are in use?

Thank you!