I don't understand why people are having trouble with this and I think David's answer missed the point and was incomplete. It's very easy to do this and the functionality has been available for a long time.
To make a folder public, click Share at the right of the folder. This will create a link. If you want, then click Access and customize the link to BoxForms or something. You can also customize access to provide an RSS feed or Embed code to embed it in your website. If you don't want to embed, you could use your own wrapper to the folder URL or make it an href link from your own website.
I shared a folder like this at https://www.box.com/public21. I did this with a free account, so it's not just an enterprise feature. The one think I couldn't find is a way to disable commenting, because I don't really want people to be able to comment on my public forms (I could delete, but it's still a pain and could be inappropriate).
If you have a paid account, you'll have more options with the custom link name.
Also, I think there's a way to do this to allow uploading files, but I can't figure out how right now.
Hope this helps!