Every hiker should carry an emergency kit. Exactly what your kit includes will vary depending on where you're hiking, your skill level, and your comfort level. (Some people might be comfortable plunging into the woods with just a knife clenched in their teeth -- I like to have a few other things with me!)
Here's a look at what I typically carry in my hiking emergency kit. The contents vary a bit depending on what kind of hike I'm on and who I'm with but, as you can see, everything* packs down into that quart-size plastic bag with plenty of room to spare. Make sure you click all the way through to the end for a peek at the most important survival tool of them all.
*Except my SAM splint -- it's too large to fit in the bag.