Wordpress - Does Wordpress have a "Form API"?
No, but it should ;)
There are several custom field class's (backend).
- wpAlchemy : https://github.com/farinspace/wpalchemy
- Meta Box Script: https://github.com/rilwis/meta-box
- My-Meta-Box: https://github.com/bainternet/My-Meta-Box
- meta-box-class: https://github.com/corycrowley/meta-box-class
- Meta Boxes Class: https://github.com/Bakke/Wordpress-Custom-Meta-Boxes-Class
For front-end forms, you probably best off with a plugin in Eugene Manuilov's link.
There is no Form API. Try to use plugin for it. Find it here: wordpress.org/extend/plugins/search.php?q=form
Another custom field library:
Custom Metaboxes and Fields for WordPress
A lot of the 'free' form plugins in the repo are very limited in functionality, but there are options: