They don't have the free and $12 and $24 plans listed on the website anymore as far as I can tell, but perhaps you are able to downgrade to one of those plans after signing up for one of the other plans.
The current signup urls are:
Maximum: https://signup.37signals.com/basecamp/Max/signup/new
Premium: https://signup.37signals.com/basecamp/Premium/signup/new
Plus: https://signup.37signals.com/basecamp/Plus/signup/new
Old Plans:
Basic: https://signup.37signals.com/basecamp/Basic/signup/new