Javascript, 18 characters
alert(btoa('ÛMx'))Update: in ES6, using a template literal can save two characters:
alert(btoa`ÛMx`)The code above is fairly easy to understand by keeping in mind that btoa converts a string into another string according to a set of well-defined rules (RFC 4648). To see how the conversion works, we're going to write the input string "ÛMx" as a sequence of binary digits, where each character is rendered as its 8-bit character code.
Input character | Û | M | x Character code (decimal) | 219 | 77 | 120 Character code (binary) | 11011011 | 01001101 | 01111000
After reorganizing the binary digits in the last row in groups of 6, we get the binary representation of 4 new numbers, corresponding to the Base64 indices of the 4 characters in the string "2014".
Base64 index (binary) | 110110 | 110100 | 110101 | 111000 Base64 index (decimal) | 54 | 52 | 53 | 56 Output character | 2 | 0 | 1 | 4
As per HTML specification, the output characters can be retrieved from their Base64 indices according to this table: http://dev.w3.org/html5/spec-LC/webappapis.html#base64-table.
If you don't care about the details, you could let the browser do the calculations for you and find out that "ÛMx" is the result of evaluating atob('2014') in Javascript.