Per https://developer.mozilla.org/en-US/docs/Web/API/WindowBase64/Base64_encoding_and_decoding and http://en.wikipedia.org/wiki/Basic_access_authentication , here is how to do Basic auth with a header instead of putting the username and password in the URL. Note that this still doesn’t hide the username or password from anyone with access to the network or this JS code (e.g. a user executing it in a browser):

$.ajax({
  type: 'POST',
  url: http://theappurl.com/api/v1/method/,
  data: {},
  crossDomain: true,
  beforeSend: function(xhr) {
    xhr.setRequestHeader('Authorization', 'Basic ' + btoa(unescape(encodeURIComponent(YOUR_USERNAME + ':' + YOUR_PASSWORD))))
  }
});

NodeJS answer:

In case you wanted to do it with NodeJS: make a GET to JSON endpoint with Authorization header and get a Promise back:

First

npm install --save request request-promise

(see on npm) and then in your .js file:

var requestPromise = require('request-promise');

var user = 'user';
var password = 'password';

var base64encodedData = Buffer.from(user + ':' + password).toString('base64');

requestPromise.get({
  uri: 'https://example.org/whatever',
  headers: {
    'Authorization': 'Basic ' + base64encodedData
  },
  json: true
})
.then(function ok(jsonData) {
  console.dir(jsonData);
})
.catch(function fail(error) {
  // handle error
});

If you are in a browser environment you can also use btoa.

btoa is a function which takes a string as argument and produces a Base64 encoded ASCII string. Its supported by 97% of browsers.

Example:

> "Basic " + btoa("billy"+":"+"secretpassword")
< "Basic YmlsbHk6c2VjcmV0cGFzc3dvcmQ="

You can then add Basic YmlsbHk6c2VjcmV0cGFzc3dvcmQ= to the authorization header.

Note that the usual caveats about HTTP BASIC auth apply, most importantly if you do not send your traffic over https an eavesdropped can simply decode the Base64 encoded string thus obtaining your password.

This security.stackexchange.com answer gives a good overview of some of the downsides.

no need to use user and password as part of the URL

you can try this

byte[] encodedBytes = Base64.encodeBase64("user:passwd".getBytes());

String USER_PASS = new String(encodedBytes);

HttpUriRequest request = RequestBuilder.get(url).addHeader("Authorization", USER_PASS).build();

PHP – curl:

$username = 'myusername';
$password = 'mypassword';
...
curl_setopt($ch, CURLOPT_USERPWD, $username . ":" . $password);
...

PHP – POST in WordPress:

$username = 'myusername';
$password = 'mypassword';
...
wp_remote_post('https://...some...api...endpoint...', array(
  'headers' => array(
    'Authorization' => 'Basic ' . base64_encode("$username:$password")
  )
));
...