How do I get a free Minecraft cape without mods?

The only way to get a free Minecraft cape without using mods is to get one from Mojang itself.

Here is the list of methods how to get a cape from Mojang:

• Take part in an official Minecraft event: Minecon
• Temporary capes (given to everybody), example: 2011 New Year Cape, given to all Minecraft players on New Year's Eve
• Personal capes (example: Turtle Cape - given to 'billyK_' for suggesting to add turtles into the game)
• For translating the game to other languages
• For creating a Realms map
• Winning certain competitions in Scrolls or Cobalt

Sadly, i did not find any mod that would enable you to have a free Minecraft cape without using Forge. However, if you really want that cape, then it may be worth it to use Forge to get one, or you can donate some money to OptiFine to get a cape (doesn't require Forge).