37id-login-form.html

<form action="https://launchpad.37signals.com/authenticate" method="post">
  <input name="product" value="YOUR-PRODUCT" type="hidden" />
  <input name="subdomain" value="YOUR-SUBDOMAIN" type="hidden" />

  <p>Username<br />
  <input name="username" id="username" type="text" /></p>

  <p>Password<br />
  <input name="password" id="password" type="password" /></p>

  <p><label><input name="remember_me" id="remember_me" value="1" type="checkbox" />
    Remember me on this computer
  </label></p>

  <p><input name="submit" value="Sign in" type="submit" /></p>
</form>

gistfile2.txt

The product and subdomain fields must be customized.

Product should be one of basecamp, backpack, campfire, or highrise.
Subdomain should be the subdomain portion of your account's URL.

Example for a Basecamp account located at http://acme.basecamphq.com:

<input name="product" value="basecamp" type="hidden" />
<input name="subdomain" value="acme" type="hidden" />

I had the same problem...

I solved in this way:
I replaced https://launchpad.37signals.com/authenticate
with
https://launchpad.37signals.com/session
(when I normally login on basecam it uses this url)
And....
Removed subdomain (not needed)

<form action="https://launchpad.37signals.com/session" method="post">
    <input name="product" value="basecamp" type="hidden" />
    <p>Username<br />
        <input name="username" id="username" type="text"  /></p>
    <p>Password<br />
        <input name="password" id="password" type="password" /></p>

    <p><label><input name="remember_me" id="remember_me" value="1" type="checkbox" />
            Remember me on this computer
        </label></p>

        <p><input name="submit" value="Sign in" type="submit" /></p>
</form>

How would we create a check to see if we are already logged in (and forward if so?). It's strange having to login every time... when you may already be logged in.