I'm surprised you haven't been prompted to upgrade your account. 37signals switched to a new login system 18 months ago which doesn't store passwords in the clear. With a new login you get a regular password reset email.
Because the newer login system requires you to move away from having any easy to remember username (eg. someperson) that only needs to be unique on a particular Basecamp instance, to picking a harder to remember new username (eg. someperson5946) that needs to be unique everywhere.