Best practice: one form per product is definitely the way to go.
Benefits:
In your specific situation
If you only ever intend to have one form element, in this case a submit button, one form for all should work just fine.
My recommendation Do one form per product, and change your markup to something like:
<form method="post" action="">
<input type="hidden" name="product_id" value="123">
<button type="submit" name="action" value="add_to_cart">Add to Cart</button>
</form>
This will give you a much cleaner and usable POST. No parsing. And it will allow you to add more parameters in the future (size, color, quantity, etc).
Note: There's no technical benefit to using
<button>vs.<input>, but as a programmer I find it cooler to work withaction=='add_to_cart'thanaction=='Add to Cart'. Besides, I hate mixing presentation with logic. If one day you decide that it makes more sense for the button to say "Add" or if you want to use different languages, you could do so freely without having to worry about your back-end code.