In the words of Harvey Danger, "If you're bored then you're boring."
There are literally thousands of things you can do without money that will burn time. You need to find the ones that will interest you, but here are a handful of suggestions:
1) Join your local library and read, attend community events, flirt with the librarian, etc
2) Look around your room, then see if you can cross the room to pick a certain thing up with your eyes closed
3) Find a shopping center that gives out free samples and patrol that mother until you are full
4) Join a LARP group (some have dues, some are free)
5) Create a secret language
6) Assign yourself or a friend various physical challenges
7) Can you balance a spoon on your nose?
8) Memorize a train schedule.
9) Participate in a community service project
10) Pet something adorable (I go to the pet shop and ask to hold the mice!)
11) Learn to cook (technically costs money for food, but you did need to eat anyway, right?)
12) Try yoga
13) Go to a public place. When people pass you across the street, pretend to squish their heads with your fingers
14) Got a box? Now it's a spaceship/pirate ship/portal to a parallel universe!
15) Get involved with a school club
16) Start attending many different churches/religious meetings. Observe the similarities and differences
17) Try to catch a fly in one hand
18) Practice long-distance spitting
19) Find and name constellations in the night sky. Make up some of your own.
20) See how far you can travel on just one foot. (Apologies if you already have use of one or fewer feet.)
21) Convince a stranger that you are foreign
22) Convince a stranger that you are famous
23) Speak only in rhyme for as long as you can stand it
24) Write. If you can't think of a damned thing, start writing about that and let every inane thought turn into written word - see how long your hand can actually keep up.
25) Make odd faces in the mirror