Cats are peculiar animals.  They have extremely sensitive stomachs, so slight changes in diet can cause big puking problems.  Also, they lick themselves, so they need to puke up hairballs on a regular basis.  And sometimes they just eat too fast or run around with a full stomach or simply think about something objectionable, so they puke.  While it's typically easy to train a cat to use a litter box for their "business," it's a different game when it comes to puke.  Here's what I believe goes through the mind of a cat when their stomach is acting up: 

1. Uh oh, I have a rumbly in my tumbly.  I'm gonna puke.
2. Is there a book or newspaper around?  If so, puke on it, because paper soaks up liquid.  If not, continue.
3. Is there anything made of a soft, absorbent material nearby?  Perhaps carpet, recently-washed laundry, or shoes?  If so, puke on them, because they'll soak up the moisture while leaving the solids intact.  If not, continue.
4. Am I on a couch or a bed?  If not, get on one.  Couches and beds are really great places to puke.  Also, the humans need to know that I puked.  Otherwise, continue.
5. If all else fails, where's the nearest high point?  The top of the stairs?  The bathroom sink?  The kitty tower?  Wherever it is, get there, and puke away from it, thus covering as much ground as possible.
6. Mission accomplished.  Man, I'm hungry.  Why don't I go eat, run around, then lick myself.

Here's some more info from a previous post.