Before doing the fix described below, you might want to try an alternate method that has been described by RadioactivePandah!:

In the game options menu, do:

• Switch to windowed mode.
  
• Change your resolution to whatever you like.
  
• Switch back to fullscreen.

In the file '<path to Steam>\SteamApps\common\Spelunky\Data\config.txt', you have the following configuration:


While those parameters are rather self-explanatory, here are a few explanations and notes:

• 'Screen_Width' is followed (on the next line) by the horizontal value (in pixels) of your wished resolution.
  
• 'Screen_Height' is followed (on the next line) by the vertical value (in pixels) of your wished resolution.
  
• The displayed image(s) will always be in the 16:9 format, no matter the resolution you did set. Extra space will be filled in black.

Here is an example of the configuration file with a resolution of 1920x1080, in full screen, with maximum full screen effects and dynamic shadows; using the english language: