application/x-www-form-urlencoded or multipart/form-data?

TL;DR

Summary; if you have binary (non-alphanumeric) data (or a significantly sized payload) to transmit, use multipart/form-data. Otherwise, use application/x-www-form-urlencoded.

The MIME types you mention are the two Content-Type headers for HTTP POST requests that user-agents (browsers) must support. The purpose of both of those types of requests is to send a list of name/value pairs to the server. Depending on the type and amount of data being transmitted, one of the methods will be more efficient than the other. To understand why, you have to look at what each is doing under the covers.

For application/x-www-form-urlencoded, the body of the HTTP message sent to the server is essentially one giant query string -- name/value pairs are separated by the ampersand (&), and names are separated from values by the equals symbol (=). An example of this would be: 

MyVariableOne=ValueOne&MyVariableTwo=ValueTwo

According to the specification:

[Reserved and] non-alphanumeric characters are replaced by `%HH', a percent sign and two hexadecimal digits representing the ASCII code of the character

That means that for each non-alphanumeric byte that exists in one of our values, it's going to take three bytes to represent it. For large binary files, tripling the payload is going to be highly inefficient.

That's where multipart/form-data comes in. With this method of transmitting name/value pairs, each pair is represented as a "part" in a MIME message (as described by other answers). Parts are separated by a particular string boundary (chosen specifically so that this boundary string does not occur in any of the "value" payloads). Each part has its own set of MIME headers like Content-Type, and particularly Content-Disposition, which can give each part its "name." The value piece of each name/value pair is the payload of each part of the MIME message. The MIME spec gives us more options when representing the value payload -- we can choose a more efficient encoding of binary data to save bandwidth (e.g. base 64 or even raw binary).

Why not use multipart/form-data all the time? For short alphanumeric values (like most web forms), the overhead of adding all of the MIME headers is going to significantly outweigh any savings from more efficient binary encoding.

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READ AT LEAST THE FIRST PARA HERE!

I know this is 3 years too late, but Matt's (accepted) answer is incomplete and will eventually get you into trouble. The key here is that, if you choose to use multipart/form-data, the boundary must not appear in the file data that the server eventually receives.

This is not a problem for application/x-www-form-urlencoded, because there is no boundary. x-www-form-urlencoded can also always handle binary data, by the simple expedient of turning one arbitrary byte into three 7BIT bytes. Inefficient, but it works (and note that the comment about not being able to send filenames as well as binary data is incorrect; you just send it as another key/value pair).

The problem with multipart/form-data is that the boundary separator must not be present in the file data (see RFC 2388; section 5.2 also includes a rather lame excuse for not having a proper aggregate MIME type that avoids this problem).

So, at first sight, multipart/form-data is of no value whatsoever in any file upload, binary or otherwise. If you don't choose your boundary correctly, then you will eventually have a problem, whether you're sending plain text or raw binary - the server will find a boundary in the wrong place, and your file will be truncated, or the POST will fail.

The key is to choose an encoding and a boundary such that your selected boundary characters cannot appear in the encoded output. One simple solution is to use base64 (do not use raw binary). In base64 3 arbitrary bytes are encoded into four 7-bit characters, where the output character set is [A-Za-z0-9+/=] (i.e. alphanumerics, '+', '/' or '='). = is a special case, and may only appear at the end of the encoded output, as a single = or a double ==. Now, choose your boundary as a 7-bit ASCII string which cannot appear in base64 output. Many choices you see on the net fail this test - the MDN forms docs, for example, use "blob" as a boundary when sending binary data - not good. However, something like "!blob!" will never appear in base64 output.

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I don't think HTTP is limited to POST in multipart or x-www-form-urlencoded. The Content-Type Header is orthogonal to the HTTP POST method (you can fill MIME type which suits you). This is also the case for typical HTML representation based webapps (e.g. json payload became very popular for transmitting payload for ajax requests).

Regarding Restful API over HTTP the most popular content-types I came in touch with are application/xml and application/json.

application/xml:

data-size: XML very verbose, but usually not an issue when using compression and thinking that the write access case (e.g. through POST or PUT) is much more rare as read-access (in many cases it is <3% of all traffic). Rarely there where cases where I had to optimize the write performance

existence of non-ascii chars: you can use utf-8 as encoding in XML

existence of binary data: would need to use base64 encoding

filename data: you can encapsulate this inside field in XML

application/json

data-size: more compact less that XML, still text, but you can compress

non-ascii chars: json is utf-8

binary data: base64 (also see json-binary-question)

filename data: encapsulate as own field-section inside json

binary data as own resource

I would try to represent binary data as own asset/resource. It adds another call but decouples stuff better. Example images:

POST /images
Content-type: multipart/mixed; boundary="xxxx" 
... multipart data

201 Created
Location: http://imageserver.org/../foo.jpg

In later resources you could simply inline the binary resource as link:

<main-resource>
 ...
 <link href="http://imageserver.org/../foo.jpg"/>
</main-resource>

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I agree with much that Manuel has said. In fact, his comments refer to this url...

http://www.w3.org/TR/html401/interact/forms.html#h-17.13.4

... which states:

The content type "application/x-www-form-urlencoded" is inefficient for sending large quantities of binary data or text containing non-ASCII characters. The content type "multipart/form-data" should be used for submitting forms that contain files, non-ASCII data, and binary data.

However, for me it would come down to tool/framework support.

What tools and frameworks do you expect your API users to be building their apps with?

Do they have frameworks or components they can use that favour one method over the other?

If you get a clear idea of your users, and how they'll make use of your API, then that will help you decide. If you make the upload of files hard for your API users then they'll move away, of you'll spend a lot of time on supporting them.

Secondary to this would be the tool support YOU have for writing your API and how easy it is for your to accommodate one upload mechanism over the other.

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Just a little hint from my side for uploading HTML5 canvas image data:

I am working on a project for a print-shop and had some problems due to uploading images to the server that came from an HTML5 canvas element. I was struggling for at least an hour and I did not get it to save the image correctly on my server.

Once I set the contentType option of my jQuery ajax call to application/x-www-form-urlencoded everything went the right way and the base64-encoded data was interpreted correctly and successfully saved as an image.

Maybe that helps someone!

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If you need to use Content-Type=x-www-urlencoded-form then DO NOT use FormDataCollection as parameter: In asp.net Core 2+ FormDataCollection has no default constructors which is required by Formatters. Use IFormCollection instead:

 public IActionResult Search([FromForm]IFormCollection type)
    {
        return Ok();
    }

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In my case the issue was that the response contentType was application/x-www-form-urlencoded but actually it contained a JSON as the body of the request. Django when we access request.data in Django it cannot properly converted it so access request.body.

Refer this answer for better understanding: Exception: You cannot access body after reading from request's data stream

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