I understand that Electric Guitars and other such pickup-based Electric string instruments have a different impedance level than that of, say, regular stereo headphones. Thus, if one plugs in their headphones directly into the instrument, its going to get damaged. To avoid this problem, one uses the ‘headphone out’ jack on their guitar amp / effects processor to connect their headphones. My question is , is there a much simpler passive device that can be put between the headphones and the guitar? I really would like to play my guitar without having to carry a bulky effects processor (which requires a power supply) or an amp.

The difference in impedances is not the problem – that could be overcome with a small transformer.

The problem is that the signal from the pick-up is simply too weak to drive ‘phones so you do need an active device (an amplifier.)

A very small, cheap and battery operated one is sold by RadioShack in the ‘States:

http://www.radioshack.com/product/index.jsp?productId=2062620&cp=&origkw=audio+amplifier&kw=audio+amplifier&parentPage=search

Another one is frequently advertised on eBay:

http://cgi.ebay.co.uk/Headphone-Amplifier-for-Audiophiles-SUPERB-SOUND-iPod_W0QQitemZ9718006711QQcategoryZ3280QQrdZ1QQcmdZViewItem

The RadioShack one is mono.
The other is stereo so it would probably be more convenient to connect both channels together at the input.