It could be free if you already have Acrobat XI and you don't mind people sending the data to you via emails.
You can use FormsCentral for Acrobat to design the form and generate a PDF and add a submit button in Acrobat to submit the form to your email address (see http://forums.adobe.com/message/5420738#5420738.) With the approach you can only collect data via PDF forms.
If you want to have the data collected via FormsCentral and/or use a web form to collect data then you would need to get a subscription to FormsCentral.
Depening on how long you need to keep the form open to collect data then you can get the montly subscription (Basic Plan) or the Yearly subscription (Plus Plan)
The Basic plan only cost $0.99 for the first month.
The free plan would work too if you only have one form BUT you can only collect 50 responses (although you can always export and delete the responses as they come in). This might be a good way for you to try out the service and see if this works better than collecting data yourself via email using only Acrobat XI and no subscription.
Hope this helps